Assignments For Class 10 Mathematics Coordinate Geometry

Assignments Assignments for Class 10

Assignments for Class 10 Mathematics Coordinate Geometry have been developed for Standard 10 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 10 Mathematics Coordinate Geometry from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 10 Mathematics Coordinate Geometry. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Coordinate Geometry book and get good marks in class 10 exams.

Question. The lines, x = 2 and y = 3 are       
(A) parallel to each other
(B) perpendicular to each other
(C) neither parallel nor perpendicular to each other
(D) none of these

Answer

B

Question. The lines, x = –2 and y = 3 intersect at the point ________.   
(A) (-2,3)
(B) (2,-3)
(C) (3,-2)
(D) (-3,2)

Answer

A

Question. The point equidistant from vertices of a triangle is called   
(A) circumcentre
(B) incentre
(C) orthocenter
(D) none of these

Answer

A

Question. The slope of the line joining the points (2, k – 3) and (4,-7) is 3. Find k.   
(A) -10
(B) -6
(C) -2
(D) 10

Answer

A

Question. The distance between the points (3, 4) and (6, –3) is.   
(A) √58
(B) √68
(C) √78
(D) √98

Answer

A

Question. If A and B are (1, 4) and (5, 2) respectively, then the co-ordinates of P when AP/PB = 3/4 is   
(A) (19/7 , 22/7)
(B) (20/7 , 21/7)
(C) (21/7 , 22/7)
(D) (21/7 , 23/7)

Answer

A

Question. If the coordinates of the mid-points of the sides of a triangle are (1, 2) (0, –1) and (2, –1). Then the sum of x coordinates of its vertices of the triangle is   
(A) 3
(B) 4
(C) 5
(D) 6

Answer

A

Question. The centre of a circle is C(2,-3) and one end of the diameter AB is A(3,5) . Find the coordinates of the other end B.   
(A) (1,-11)
(B) (5,2)
(C) (1,8)
(D) none of these

Answer

A

Question. Find λ , if the line 3x – λy + 6 = 0 passes through the point (–3,4).   
(A) 3/4
(B) -3/4
(C) 4/3
(D) -4/3

Answer

B

Question. Find the area of the triangle formed by the line 5x – 3y + 15 = 0with coordinate axes.   
(A) 15cm2
(B) 5 cm2
(C) 8 cm2
(D) 15/2 cm2

Answer

D

Question. The point P lying in the fourth quadrant which is at a distance of 4 units from X-axis and 3 units from Y-axis is__________.   
(A) (4,-3)
(B) (4,3)
(C) (3,-4)
(D) (-3,4)

Answer

C

Question. In what ratio does the line 4x+3y -13 = 0 divide the line segment joining the points (2, 1) and (1, 4)?   
(A) 3 : 2 internally
(B) 2 : 3 externally
(C) 2 : 3 internally
(D) 3 : 2 externally

Answer

C

Question. The points on X-axis which are at a distance of 13 units from (-2,3) is ________.   
(A) (0,0), (-2,-3)
(B) (0,0), (-4,0)
(C) (0,0), (2,3)
(D) none of these

Answer

B

Question. If (5, 3), (4, 2) and (1, –2) are the mid points of sides of triangle ABC, then the area of ΔABCis   
(A) 2 sq. units
(B) 3 sq. units
(C) 1 sq. units
(D) 4 sq. units

Answer

A

Question. The points (a,b +c), (b,c +a) and (c,a + b)   
(A) are collinear
(B) form a scalene triangle
(C) form an equilateral triangle
(D) none of these

Answer

A

Assignment for Class 10 Mathematics Coordinate Geometry Set A
Assignment for Class 10 Mathematics Coordinate Geometry Set B
Assignment for Class 10 Mathematics Coordinate Geometry Set C
Assignment for Class 10 Mathematics Coordinate Geometry Set D
Assignment for Class 10 Mathematics Coordinate Geometry Set E
Assignment for Class 10 Mathematics Coordinate Geometry Set F
Assignment for Class 10 Mathematics Coordinate Geometry Set G
Assignment for Class 10 Mathematics Coordinate Geometry Set H
Assignment for Class 10 Mathematics Coordinate Geometry Set I
Assignment for Class 10 Mathematics Coordinate Geometry Set J
Assignment for Class 10 Mathematics Coordinate Geometry Set K
Assignment for Class 10 Mathematics Coordinate Geometry Set L
Assignment for Class 10 Mathematics Coordinate Geometry Set M
Assignment for Class 10 Mathematics Coordinate Geometry Set N
Assignment for Class 10 Mathematics Coordinate Geometry Set O
Assignment for Class 10 Mathematics Coordinate Geometry Set P
Assignment for Class 10 Mathematics Coordinate Geometry Set Q
Assignment for Class 10 Mathematics Coordinate Geometry Set R
Assignment for Class 10 Mathematics Coordinate Geometry Set S
Assignment for Class 10 Mathematics Coordinate Geometry Set T
Assignment for Class 10 Mathematics Coordinate Geometry Set U
Assignment for Class 10 Mathematics Coordinate Geometry Set V
Assignment for Class 10 Mathematics Coordinate Geometry Set W
Assignment for Class 10 Mathematics Coordinate Geometry Set X
Assignment for Class 10 Mathematics Coordinate Geometry Set Y
Assignment for Class 10 Mathematics Coordinate Geometry Set Z

Coordinate Geometry

A point in 2-D plane (let’s say XY plane) is represented by its coordinates (x,y)
Here x is the distance of a point from the x-axis and is called y-coordinate.
y is the distance of a point from the and is called its .

Distance Formula : the distance between the points  P(x1,y1) and Q(x2,y2) is PQ=

Assignments For Class 10 Mathematics Coordinate Geometry

This is called distance formula. F

Assignments For Class 10 Mathematics Coordinate Geometry

Area of a triangle : the area of ABC is the numerical value of the expression F

Assignments For Class 10 Mathematics Coordinate Geometry

Section Formula : the coordinates of the point P(x,y) which divides the line segment joining the points A(x1,y1) and B(x2,y2) internally, in the ratio m1:mare

Assignments For Class 10 Mathematics Coordinate Geometry

This is known as section formula. F

Assignments For Class 10 Mathematics Coordinate Geometry

Special Case -: if P is mid point then m1:m=1:1

Now, the coordinates of mid point 

Assignments For Class 10 Mathematics Coordinate Geometry

In order to prove that a given figure is a :
i) Square, prove that four sides are equal and the diagonals are equal.
ii) Rhombus, prove that the four sides are equal.
iii) Rectangle, prove the opposite sides are equal and the diagonals are also equal.
iv) Parallelogram, prove that the opposite sides are equal.
The point of intersection of the medians of a triangle is called its called its centroid. The coordinates of the centroid of the triangle whose are (x1,y1) ,(x2,y2) and (x3,y3) are given by

Assignments For Class 10 Mathematics Coordinate Geometry

For three points to be collinear,
i) The sum of the distances between two pairs of points is equal to the distance third pair of points.
Three given points A(x1,y1) ,B(x2,y2) and C(x3,y3) are collinear if ABC =0.

Question. Find the condition that the point (x, y) may lie on the line joining (3, 4) and (-5, – 6).   
Solution. Since the point P (x, y) lies on the line joining A (3, 4) and B (-5, -6). Therefore, P, A andB are collinear points. 

Assignments For Class 10 Mathematics Coordinate Geometry

Hence, the point (x, y) lies on the line joining (3,4) and (-5, -6), if 5x – 4y+1 = 0

Question. Show that the points A(3, 5), B(6, 0), C(1, -3) and D (-2, 2) are the vertices of a square ABCD.   
Solution. Let A( 3,5), B(6, 0), C(1, -3 ) and D(-2, 2) be the angular points of a quadrilateral ABCD. Join AC and BD

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Thus, ABCD is a quadrilateral in which all sides are equal and the diagonals are equal.
Hence, quad. ABCD is a square.

Question. If P (x, y) is any point on the line joining the points A(a,0) and B(0, b), then show that x/a + y/b = 1   
Solution. It is given that the point P (x, y) lies on the line segment joining points A (a, 0) and B (0,
b).Therefore, points P (x, y), A (a, 0) and B (0, b) are collinear points.

Assignments For Class 10 Mathematics Coordinate Geometry

Question. A (4, 2), B (6, 5) and C (1, 4) are the vertices of ΔABC.   
Solution.

Assignments For Class 10 Mathematics Coordinate Geometry

i. The median from A meets BC in D. Find the coordinates of the point D.

i. Median AD of the triangle will divide the side BC in two equal parts. So D is the midpoint of side BC.

Assignments For Class 10 Mathematics Coordinate Geometry

ii. Find the coordinates of point P on AD such that AP : PD = 2:1.

Assignments For Class 10 Mathematics Coordinate Geometry

iii. Find the coordinates of the points Q and R on medians BE and CP respectively such that BQ : QE = 2 :1 and CR: RF =2: 1.

Median BE of the triangle will divide the side AC in two equal parts. So E is the midpoint of side AC.

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

iv. What do you observe? 
Now we may observe that coordinates of point P, Q are same. So, all these are representing same point on the plane i.e. centroid of the triangle.

Question. Find the lengths of the medians of a ΓABC whose vertices are A(0, -1) B(2, 1) and C(0,3).   
Solution. Let D, E, F be the midpoint of the side BC, CA and AB respectively in ΔABC

Assignments For Class 10 Mathematics Coordinate Geometry

Question. The area of triangle formed by the points (p, 2 – 2p), (1, p, 2 p ) and (-4 -p, 6 – 2p) is 70 sq. units. How many integral values of p are possible.   
Solution.

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the coordinates of the centroid of a triangle whose vertices are (0,6), (8,12) and (8,0).   
Solution. Coordinates of the centroid of a triangle whose vertices are (x1, y1), (x2, y2), (x3, y3) are

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Point A is on x-axis, point B is on y-axis and the point P lies on line segment AB, such that P (4, – 5) and AP : PB = 5 : 3. Find the coordinates of point A and B.   
Solution. Let coordinates of A are (x, 0) and coordinates of B are (0, y)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. If the points A(x, 2), B(- 3, – 4), C(7, – 5) are collinear, then find the value of x.   
Solution. Since the points are collinear, then,
Area of triangle = 0

Assignments For Class 10 Mathematics Coordinate Geometry

Practice Exercise :

Question. Prove that(4,-1),(6,0),(7,2)&(5,1) are the vertices of a rhombus .Is it a square?
Solution. Proof

Question. Find the coordinates of a point A, where AB is diameter of a circle whose Centre is(2,-3)and B is(1,4)
Solution. (3,-10)

Question. Find the centroid of triangle whose vertices are (3,-7), (-8,6) and (5,10).
Solution. (0,3)

Question. If A (-2,4),B(0,0),C(4,2) are the vertices of a ΔABC, then find the length of median through the vertex A.
Solution. 5 units

Question. Find the area of the triangle formed by joining the mid points of the sides of the triangle whose vertices are (0,-1),(2,1) and (0,3).Find the ratio of this area to the area of the given triangle.
Solution. 1:4

Question. Determine the ratio in which the point P(a,-2) divides the line joining of points(-4,3) and B(2,-4).Also find the value of a.
Solution. a=2/7

Question. If the point C(-1,2) divides internally the line segment joining A(2,5)and in the ratio 3:4. Find the Co- ordinates of B.
Solution. B(-5,-2)

Question. Show that points (1,1), (4,4) ,(4,8)and (1,5) are the vertices of a parallelogram.
Solution. Proof

Question. Find the value of p, for which the points(-1,3),(2,p) & (5,-1)are collinear
Solution. p=1

Question. If the points(-1,3),(1,-1)and(5,1)are the vertices of a triangle .Find the length of the median through the first vertex.
Solution. 5

Question. Find the center of a circle passing through the points (6,-6), (3,-7)and(3,3).
Solution. (3,-2)

Question. If the distance between the points (3,0) and (0,y)is 5 units and y is positive ,what is the value of y?
Solution. 4

Question. If the points(x ,y),(-5,-2)and(3,-5)are collinear r, then prove that 3x+8y+31=0.
Solution. Proof

Question. A line intersects y–axis and x-axis at the points P and Q respectively. If (2,-5) is the midpoint of PQ, then find the coordinates of P and Q respectively.
Solution. (0,-10) and(4,0)

Question. Show that the three points (a,a) ,(-a,-a) &(-a√3 , a√3) are the vertices of an equilateral triangle.
Solution. Proof

Question. Find the value of k, if the point P (2, 4) is equidistant from the points (5, k) and (k, 7).
Solution. K=3

Question. If the point A(0,2)is equidistant from the points B (3,p) and C(p,5),find p .Also find the length of AB.
Solution. P=1, AB=√10

Question. Find the distance between the points A and B in the following : A(a, 0), B(0, a)   
Solution. A(a, 0), B(0, a)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the perpendicular distance of A(5,12) from the y-axis.   
Solution. The point on the y-axis is (0,12)
Distance between (5,12) and (0,12)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the distance of the point (- 4, – 7) from the y-axis.   
Solution. Points are (- 4, – 7) and (0, – 7)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the distance between the points: A(-6, -4) and B(9, -12)   
Solution. The given points are A(-6, -4) and B(9, -12)
Then, (x1 = -6, y1 = -4) and (x2 = 9, y2 = -12)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Show that four points (0, -1), (6, 7), (-2, 3) and (8, 3) are the vertices of a rectangle. Also,find its area.   Solution.Let A (0 – 1), B (6, 7), C (-2, 3) and D (8, 3) be the given points. Then,

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the co-ordinates of the points of trisection of the line segment joining the points A(1,- 2) and B(- ,4). 
Solution.

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the distance between the points A and B in the following:A(1,-3), B(4, 1)   
Solution. A(1, -3), B(4, 1)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b. 

Assignments For Class 10 Mathematics Coordinate Geometry

Solution. Let A(a, -11), B(5, b), C(2, 15) and D(1, 1) be the given points.
We know that diagonals of parallelogram bisect each other.
Therefore, Coordinates of mid-point of AC = Coordinates of mid-point of BD

Assignments For Class 10 Mathematics Coordinate Geometry

Hence value of a and b is equal to 4 and 3 respectively.

Question. Find the coordinates of the point , where the line x – y = 5 cuts Y-axis.  
Solution. x – y = 5 is a given line
x – y = 5 cuts Y-axis.
Put x = 0 in the equation of line x- y = 5
⇒ (0) – y = 5
⇒ y = – 5
Therefore , the point is (0,-5)cuts x – y = 5 at Y-axis..

Question. If the point A(2, –4) is equidistant from P(3, 8) and Q(–10, y) then find the values of y. Also find distance PQ.   
Solution. According to the question,we are given that,
PA = QA
⇒ PA2 = QA2
⇒ (3 – 2)2 + (8 + 4)2 = (–10 – 2)2 + (y + 4)2
⇒ 12 + 122 = (–12)2 + y2 + 16 + 8y
⇒ y2 + 8y + 16 – 1 = 0
⇒ y2 + 8y + 15 = 0
⇒ y2 + 5y + 3y + 15 = 0
⇒ y(y + 5) + 3(y + 5) = 0
⇒ (y + 5) (y + 3) = 0
⇒ y + 5 = 0 or y + 3 = 0
⇒ y = –5 or y = –3
So, the co–ordinates are P(3, 8), Q1(–10, –3), Q2(–10, –5).

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the value of ‘k’ if the points (7, –2), (5, 1), (3, k) are collinear.   
Solution. (7, –2), (5, 1), (3, k)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the perimeter of a triangle with vertices (0, 4), (0,0) and (3,0).   
Solution. Here, A→ (0,4),B→ (0,0),C→ (3,0)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the area of a quadrilateral PQRS whose vertices area P(- 5, 7), Q(- 4, – 5), R (-1, – 6) and S(4, 5).   
Solution. Area PQRS = ar PQS + ar QRS

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Hence, area PQRS = 53 + 19 = 72 sq. units

Question. The point R divides the line segment AB where A(-4, 0), B(0, 6) are such that AR =3/4 A B. Find the coordinates of R. 
Solution.

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Question. Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the join of the middle points of its diagonals meet in a point and bisect one another. 
Solution. Let OBCD be the quadrilateral P, Q, R, S be the mid-points of OB, CD, OD and BC.  

Assignments For Class 10 Mathematics Coordinate Geometry

Let the coordinates of O,B, C, D are (0, 0), (x, 0), (x, y) and (0, y)
Coordinates of P are (x/2 ,0)
Coordinates of Q are (x/2 , y)
Coordinates of R are (0,y/2)
Coordinates of S are (x , y/2)
Coordinates of mid-point of PQ are

Assignments For Class 10 Mathematics Coordinate Geometry

Since, the coordinates of the mid-point of PQ = coordinates of mid-point of RS.
PQ and RS bisect each other.

Question. In the given triangle ABC as shown in diagram D, E and F are the mid-points of AB, BC and AC respectively. Find the area of ΔDEF.   
Solution.

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the value of m for which the points with coordinates (3, 5), (m, 6) and (1/2 , 15/2) are collinear.   
Solution. If points are collinear, then one point divides the other two in the same ratio.
Let point (m, 6) divides the join of (3, 5) and (1/2 , 15/2) in the ratio k: 1.

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Question. If origin is the mid-point of the line segment joined by the points (2, 3) and (x, y) then find the value of (x, y).   
Solution.

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the centroid of the triangle whose vertices are given below: (3, -5), (-7, 4), (10,-2).   
Solution. The given vertices of triangle are (3, -5), (-7, 4) and (10, -2).
Let (x, y) be the coordinates of the centroid. Then

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the number of points on x-axis which are at a distance of 2 units from (2, 4).   
Solution. Distance of the point (2, 4) from x-axis is 4 units. There is no point on x-axis which is at a distance of 2 units from the given point.

Question. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: 
(-1, -2), (1, 0), (-1, 2), (-3, 0) (4)
Solution. (-1, -2), (1, 0), (-1, 2), (-3, 0)
Let A→ (-1, -2), B→ (1, 0)
C→ (-1, 2) and D→ (-3, 0)

Assignments For Class 10 Mathematics Coordinate Geometry

Since AB = BC = CD = DA (i.e., all the four sides of the quadrilateral ABCD are equal) and AC = BD (i.e. diagonals of the quadrilateral ABCD are equal). Therefore, ABCD is a square.

Question. Find the area of the triangle with vertices (0 ,0) (6 ,0) and (0 ,5).   
Solution. We have to find the area of the triangle with vertices (0 ,0) (6 ,0) and (0 ,5).
Area of triangle

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Prove that the coordinates of the centroid of a triangle ABC, with vertices A(x1, y1), B(x2, y2) and C(x3, y3) are given by (x1 + x2 + x3 /3 , y1 + y2 + y3 /3)  12
Solution. Let the coordinates of vertices of ΔABC be A(x1, y1), B(x2, y2) and C(x3, y3) respectively. Let D be the midpoint of BC.
Using section formula, coordinates of D will be

Assignments For Class 10 Mathematics Coordinate Geometry

Now since centroid G will divide the line joining A and D in the ratio of 2 : 1, therefore again using section formula, coordinates of G will be

Assignments For Class 10 Mathematics Coordinate Geometry

Question. The centre of a circle is (2a, a -7). Find the values of a, if the circle passes through the point (11, -9) and has diameter 10√2 units. 
Solution. Diameter of a circle = 10√2 units
⇒ Radius of a circle =  5√2 units
Let the centre of a circle be O(2a, a – 7) which passes through the point P(11, -9).
⇒ OP is the radius of the circle.
⇒ OP = 5√2 units
⇒ OP2 = (5√2)2
⇒ (11 – 2a)2 + (-9 – a + 7)2 = 50
⇒ 121 + 4a2 – 44a + (-2 – a)2 = 50
⇒ 121 + 4a2 – 44a + 4 + a2 + 4a = 50
⇒ 5a2 – 40a + 125 = 50
⇒ 5a2 – 40a + 75 = 0
⇒ a2 – 8a + 15 = 0
⇒ a2 – 5a – 3a + 15 = 0
⇒ a(a – 5) -3(a – 5) =0
⇒ (a – 5)(a – 3) = 0
⇒ a – 5 = 0 or a – 3 = 0
⇒ a = 5 or a = 3

Question. Find the area of the rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.   
Solution. Let A (3, 0), B (4, 5), C (-1, 4) and D (-2, -1)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. If the points P (-3, 9), Q (a, b) and R (4, -5) are collinear and a + b = 1, find the values of a and b.   
Solution. It is given that the points P (-3, 9), Q (a, b) and R(4,-5) are collinear.

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the area of a triangle ABC with A(1, – 4) and mid-points of sides through A being (2, -1) and (0, -1).   1
Solution.

Assignments For Class 10 Mathematics Coordinate Geometry

Question. If the points (0, 0), (1, 2) and (x, y) are collinear,then find x.   
Solution. The points are collinear, then area of triangle = 0

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the lengths of the medians of a ΔABC having vertices at A (0, -1), B (2, 1) and C (0, 3).   
Solution.

Assignments For Class 10 Mathematics Coordinate Geometry

Let A(0, -1), B(2, 1) and C(0, 3) be the given points.

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the distance of the point (α ,β) from y-axis.      
Solution. Distance of the point (α ,β) from y-axis is the positive value of its x-coordinate.
∴ Distance = lαl

Question. If the centre of circle is (2a, a – 7) then find the values of a if the circle passes through the point (11, –9) and has diameter 10√2 units.   
Solution.

Let C(2a, a – 7) be the centre of the circle and it passes through the point P(11, –9).

Assignments For Class 10 Mathematics Coordinate Geometry

∴ PQ = 10√2
⇒ CP = 5√2
⇒ CP2 = (5√2)2 = 50
⇒ (2a – 11)2 + (a – 7 + 9)2 = 50
⇒ (2a)2 + (11)2 – 2(2a) (11) + (a + 2)2 = 50
⇒ 4a2 + 121 – 44a + (a)2 + (2)2 + 2(a)(2) = 50
⇒ 5a2 – 40a + 125 = 50
⇒ a2 – 8a + 25 = 10
⇒ a2 – 8a + 25 – 10 = 0
⇒ a2 – 8a + 15 = 0
⇒ a2 – 5a – 3a + 15 = 0
⇒ a(a – 5) –3(a – 5) = 0
⇒ (a – 5) (a – 3) = 0
⇒ a – 5 = 0 or a – 3 = 0
⇒ a = 5 or a = 3
Hence, the required values of a are 5 and 3.

Question. If the centre and radius of circle is (3, 4) and 7 units respectively, then what is the position of the point A(5,8) with respect to circle?   
Solution. Distance of the point, from the centre

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the coordinates of the centre of the circle passing through the points (0, 0), (-2, 1) and (-3, 2). Also, find its radius.   

Assignments For Class 10 Mathematics Coordinate Geometry

Solution. Let P (x, y) be the centre of the circle passing through the points O (0, 0), A (-2, 1) and B (-3, 2). Then,

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Question. If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, -3) and (3,4), find the vertices of the triangle. 
Solution. Let A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of
Let D(1, 1), E(2, -3) and F(3, 4) be the mid-points of sides BC, CA and AB respectively.
Since, D is the mid-point of BC
Similarly E and F are the mid-points of CA and AB respectively.
⇒ x1 + x2 = 6 and y1 + y2 = 8 …(iii)
From (i), (ii) and (iii) we get
x2 + x3 + x1 + x3 + x1 + x2 = 2 + 4 + 6
and, y2 + y3 + y1 + y3 + y1 + y2 = 2 +(-6) + 8
⇒ 2(x1 + x2 + x3) = 12 and 2(y1 + y2 + y3) = 4
⇒ x1 + x2 + x3 = 6 and y1 + y2 + y3 = 2 …(iv)
From (i) and (iv) we get
x1 + 2 = 6 and y1 + 2 = 2
⇒ x1 = 6 – 2 y1= 2 – 2
⇒ x1 = 4 y1 = 0
So the coordinates of A are (4, 0)
From (ii) and (iv) we get
x2 + 4 = 6 and y2 + (-6) = 2
⇒ x2 = 2 ⇒ y2 – 6 = 2
⇒ y2 = 8
So the coordinates of B are (2, 8)
From (iii) and (iv) we get
6 + x3 = 6 and 8 + y3 = 2
⇒ x3 = 6 – 6 ⇒ y3 = 2 – 8
⇒ x3 = 0 ⇒ y3 = -6
So the coordinates of c are (0, -6)
Hence, the vertices of triangle ABC are:
A(4, 0), B(2, 8) and C(0, -6)

Question. Find the distance between the points P (-4, 7) and Q(2, -5).   
Solution. The given points are P (-4, 7) and Q(2, -5).
Then, x1 = -4, y1 = 7 and x2 = 2, y2 = -5.

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the point on the X-axis which is equidistant from the points (-1,0) and (5,0)     
Solution. Let A(x,o) be any point on the X-axis , which is equidistant from points (-1,0) and (5,0).
⇒ (x + 1)2 = (x – 5)2
A(x,o) be any point on the X-axis , which is equidistant from points (-1,0) and (5,0).
⇒ x2 + 2x + 1 = x2 – 10x + 25
⇒ 2x + 1 = -10x + 25
⇒ 2x + 10x = 25 – 1
⇒ 12x = 24

Question. Find value(s) of y for which the distance between the points P (2, –3) and Q (10, y) is 10 units.
Solution. Let P (2, –3) and Q (10, y) be the two given points such that PQ = 10.
∴ PQ = √(10 – 2)2 + (y + 3)2 = 10 (given)
⇒ PQ2 = 64 + y2 + 6 y + 9 = 100
⇒ y2 + 6y – 27 = 0 ⇒ y2 + 9y – 3y – 27 = 0
⇒ y (y + 9) – 3 (y + 9) = 0 ⇒ (y + 9) (y – 3) = 0
⇒ y = – 9 or y = 3 Ans.

Question. Find the ratio in which the join of (–3, 10) and (6, –8) is divided by (–1, 6).   
Solution. Let the given points be A(–3, 10), B(6, –8) and C(–1, 6).

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Question. Prove that the points (2, –2), (–3, 8) and (–1, 4) are collinear.   
Solution. Let Δ be the area of the triangle formed by given three points A(2, –2), B(–3, 8) and C(–1, 4).

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Show that the points (1, –1), (5, 2) and (9, 5) are collinear.    
Solution. Let A(1, –1), B(5, 2) and C(9, 5) be the given points.

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, –2) and (2, –2). Also, find its circum-radius.
Solution. We know circumcentre of a triangle is equidistant from the vertices of a triangle.
Let A(8, 6), B(8, –2) and C(2, –2) be the vertices of a given triangle and let P(x, y) be the circumcentre of this triangle. Then,
PA = PB = PC
⇒ PA2 = PB2 = PC2
Now, PA2 = PB2
⇒ (x– 8)2 + (y – 6)2 = (x – 8)2 + (y + 2)2
⇒ x2 + y2 – 16x – 12 y + 100 = x2 + y2 – 16x + 4y + 68
⇒ 16y = 32 ⇒ y = 2.
and PB2 = PC2
⇒ (x – 8)2 + (y + 2)2 = (x – 2)2 + (y + 2)2
⇒ x2 + y2 – 16x + 4y + 68 = x2+ y2 – 4x + 4y + 8
⇒ 12x = 60 ⇒ x = 5
So, the coordinates of the circumcentre P are (5, 2).
Also, circum-radius = PA = PB = PC
√(5 – 8)2 + (2 – 6)2  = √(-3)2 + (-4)2
√9 + 16 = √25 = 5 units Ans.

Question. Find the distance between the points :
(i) A (0, 0), B (–5, 12)
(ii) A (5, –8), B(–7, –3)

(iii) P (cos α, –sin α), Q( – cos α, sin α)
(iv) P (a + b, a – b), Q (a – b, a + b)
Solution. (i) AB = √(-5 – 0)2 + (12 – 0)2

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the area of the quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2), (2, 3).     
Solution. Let A(–4, –2), B(–3, –5), C(3, –2) and D (2, 3) be the given points.
Now, area of quad. ABCD = ar (ΔABD) + ar (ΔBCD)
For ar (ΔABD) : A(–4, –2), B(–3, –5), D(2, 3)

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Check whether (5, –2), (6, 4) and (7, –2) are the vertices of an isosceles triangle.
Solution. Let A(5, –2), B(6, 4) and C(7, –2) be the vertices of a ΔABC.
AB = √(6 – 5)2 + (4 + 2)2 = √12 + 62 = √ 1 + 36 = √37

Assignments For Class 10 Mathematics Coordinate Geometry
Assignments For Class 10 Mathematics Coordinate Geometry

Question. If A(5, –1), B(–3, –2) and C(–1, 8) are the vertices of ΔABC, find the length of medians through A and the coordinates of the centroid.   
Solution. Let AD be the median through the vertex A of ΔABC. Then, D is the mid-point of BC. So, the coordinates of D are (-3/2 , -2 + 8/2) i.e. (–2, 3).

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Show that (1, –2), (3, 0), (1, 2) and (–1, 0) are the vertices of a square.   
Solution. Let A(1, –2), B(3, 0), C(1, 2) and D(–1, 0) be the given points.

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the area of the triangle whose vertices are (–5, –1), (3, –5), (5, 2).   
Solution. Let A(–5, –1), B(3, –5), C(5, 2) be the given points.

Assignments For Class 10 Mathematics Coordinate Geometry

Question. Find the co-ordinates of the points of trisection of the line joining the points (4, –1) and (–2, –3).   
Solution. Let C and D be the points of trisection of AB

Assignments For Class 10 Mathematics Coordinate Geometry

Assignments for Class 10 Mathematics Coordinate Geometry as per CBSE NCERT pattern

All students studying in Grade 10 Mathematics Coordinate Geometry should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics Coordinate Geometry exam for standard 10. We have made sure that all topics given in your textbook for Mathematics Coordinate Geometry which is suggested in Class 10 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

Some advantages of Free Assignments for Class 10 Mathematics Coordinate Geometry

  1. Solving Assignments for Mathematics Coordinate Geometry Class 10 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
  2. By solving one assignments given in your class by Mathematics Coordinate Geometry teacher for class 10 will help you to keep in touch with the topic thus reducing dependence on last minute studies
  3. You will be able to understand the type of questions which are expected in your Mathematics Coordinate Geometry class test
  4. You will be able to revise all topics given in the ebook for Class 10 Mathematics Coordinate Geometry as all questions have been provided in the question banks
  5. NCERT Class 10 Mathematics Coordinate Geometry Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
  6. Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 10 Mathematics Coordinate Geometry teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 10 Mathematics Coordinate Geometry Assignments PDF.

Assignments For Class 10 Mathematics Coordinate Geometry
Where can I download free Assignments for Class 10 Mathematics Coordinate Geometry ?

You can download free assignments for class 10 Mathematics Coordinate Geometry from https://www.assignmentsbag.com

I want free printable assignments with questions and answers for Mathematics Coordinate Geometry for Standard 10, where can I get them ?

You can get free PDF downloadable assignments for Grade 10 Mathematics Coordinate Geometry from our website which has been developed by teachers after doing extensive research in each topic.

Can I get assignments and question banks for other subjects in Class 10 ?

On our website we have provided assignments for all subjects in Grade 10, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

I want practice assignments for all topics in my Class 10 Mathematics Coordinate Geometry Textbook, where can I get it ?

You can easily get question banks, topic wise notes and questions and other useful study material from https://www.assignmentsbag.com without any charge

Are all assignments available for free and in PDF format ?

Yes all test papers for Mathematics Coordinate Geometry Class 10 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

What is the best website to download free assignments for Class 1 to Class 12 for all subjects ?

https://www.assignmentsbag.com is the best portal to download all assignments for all classes without any charges.