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### Math Assignment Class X Ch-7 | Coordinate Geometry

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**Math Assignment, Class X,**

**Chapter 7 Coordinate Geometry**

**Extra questions of chapter 7 class 10 Coordinate Geometry with answer and hints to the difficult questions. Important and useful math assignment for the students of class 10****For better results**

**Students should learn all the basic points of Coordinate Geometry****Student should revise N C E R T book thoroughly with examples.****Now revise this assignment. This assignment integrate the knowledge of the students.**

# ASSIGNMENT FOR 10 STANDARD

COORDINATE GEOMETRY

Question 1Find the distance between the following points:-

a) (-6,7) and (-1,-5) Ans [13]

b) (a,0) & (0,b) Ans []

c) (+1,1) & (0,) Ans []

d) (a + b, a - b) & (a - b, a + b) Ans [b]

Question 2

Find the distance of the following points from the origin:-

a) (5, -12) Ans [13]

b) (-5, 5) Ans [5 ]

c) (-4, -6) Ans [2]

Find the value of k for which the following points are collinear:

(a) (3,2), (4, k), (5,3) Ans [5/2]

b) (3,5), (m, 6), (1/2, 15/2) Ans [2]

c) (2,5), (k,11/2), (4,6) Ans [3]

Question 4

Find the ratio in which the point P(b, 1) divides the join of A(7, -2) and B(-5, 6). Also find b

Find the ratio in which the point P(b, 1) divides the join of A(7, -2) and B(-5, 6). Also find b

Ans [3:5, b = 5/2,]

Find the ratio in which the point P(a, -2) divides the join of A(-4, 3), & B(2, -4). Also find a.

Ans [5 : 2, a = 2/7]

Question 6

The coordinates of the mid- point of the line joining the points (2p + 2, 3) & (4, 2q + 1) is (2p, 3q). Find the value of p & q.

Ans [3, 1]

The coordinates of the mid- point of the line joining the points (2p + 2, 3) & (4, 2q + 1) is (2p, 3q). Find the value of p & q.

Ans [3, 1]

If A (6,-1), B(1,3), C (k,8) are such that AB = BC. Then find the value of k

Ans [k = 5, -3]

Question 8

Find the coordinates of the point equidistant from the A(5, 8), B(5, -5),and C (1, -5) [3, 3/2]

Find the coordinates of the point equidistant from the A(5, 8), B(5, -5),and C (1, -5) [3, 3/2]

Question 9

Find the type of quadrilateral formed by:-

a) A(2, -2), B(14, 10), C(11, 13), D(-1, 1) Ans
[Rectangle]

b) A(0,-2), B(3,1), C(0,4), D(-3,1) Ans [Square]

c) A(-3,5), B(3,1), C(0,3), D(-1,-4) Ans [No]

d) A(4,5), B(7,6), C(4,3), D(1,2) Ans
[Parallelogram]

e) A(3,0), B(4,5), C(-1,4), D(-2,-1) Ans [Rhombus]

Question 10

Find the area of the quadrilateral formed in question 9.

Question 11

Find p if A(6,1), B(8,2), C(9,4), D(p,3) are the vertices of a parallelogram

Question 13

In what ratio the line segment joining the points A(-2,-3) & (3,7) is divided by the y-axis. Also find the coordinates of the point of division.

Question 19

Coordinates of the mid points of sides of a triangle are A(1,1), B(2,-3), C(3,4). Find the centroid of the triangle ABC.

Question 20

If A(2,1), B(3,4), C(0,1) are three consecutive vertices of parallelogram. Find the 4th vertex.

Ans [-1,-2]

Question 21

If the coordinates of the mid –points of the sides of a triangle are (1,1), (2,-3), and (3,4).Find the coordinates of the centroid of the triangle.

Question 31

Show that the point p(-4, 2) lies on the line segment joining the points A(-4,6) & B(-4,-6)

Question 32

The points A(2, 9), B(a, 5), C(5, 5)are the vertices of a right angled triangle at B. Find a and the area of triangle ABC

Find the area of the quadrilateral formed in question 9.

Question 11

Find p if A(6,1), B(8,2), C(9,4), D(p,3) are the vertices of a parallelogram

Ans [p = 7]

Question 12

The mid- point of the line segment joining (2a+4) & (-2,3b) is (1,2a+1). Find the value of a & b.

The mid- point of the line segment joining (2a+4) & (-2,3b) is (1,2a+1). Find the value of a & b.

Ans [a = b = 2]

Question 13

In what ratio the line segment joining the points A(-2,-3) & (3,7) is divided by the y-axis. Also find the coordinates of the point of division.

Ans [2 : 3, point of division (0,1)]

Question 14

If A(5,-1), B(-3,-2), C(-1,8)are the vertices of triangle ABC. Find the length of the median through A and the centroid of the triangle .

If A(5,-1), B(-3,-2), C(-1,8)are the vertices of triangle ABC. Find the length of the median through A and the centroid of the triangle .

Ans [] , (1/3, 5/3)

Question 15

In what ratio does the line x-y-2 = 0 divides the line segment joining (3,-1)& (8,9) If the points A(x, y), B(-5, 7) and C(-4, 5) are collinear then show that 2x + y + 3 = 0

In what ratio does the line x-y-2 = 0 divides the line segment joining (3,-1)& (8,9) If the points A(x, y), B(-5, 7) and C(-4, 5) are collinear then show that 2x + y + 3 = 0

Ans [2 : 3]

Question 16

Prove that the points A(0,0), B(5,5), C(-5,5)are the vertices of a right isosceles triangle.

Prove that the points A(0,0), B(5,5), C(-5,5)are the vertices of a right isosceles triangle.

Question 17

Find the value of p for which A(-5,1), B(1,p), C(4,-2) are collinear

Find the value of p for which A(-5,1), B(1,p), C(4,-2) are collinear

Ans [p = -1]

Question 18

Find the centroid of the following points:-

a) A(4,7), B(2,1), C(3,6) Ans [3, 14/3]

b) A(2,3), B(4,5), C(3,4) Ans [3,4]

Question 19

Coordinates of the mid points of sides of a triangle are A(1,1), B(2,-3), C(3,4). Find the centroid of the triangle ABC.

Ans [2,2/3]

Question 20

If A(2,1), B(3,4), C(0,1) are three consecutive vertices of parallelogram. Find the 4th vertex.

Ans [-1,-2]

Question 21

If the coordinates of the mid –points of the sides of a triangle are (1,1), (2,-3), and (3,4).Find the coordinates of the centroid of the triangle.

Ans 2, 2/3

Question 22

Find the length of the median of a triangle whose vertices are A(-1, 3), B(1, -1), C(5, 1)

Ans [5, , 5]

Question 23

Find the ratio in which the line segment joining the points (-10,2), & (3,-5) is divided by y-axis

Question 22

Find the length of the median of a triangle whose vertices are A(-1, 3), B(1, -1), C(5, 1)

Ans [5, , 5]

Question 23

Find the ratio in which the line segment joining the points (-10,2), & (3,-5) is divided by y-axis

Ans [10:3]

Question 24

If A(1,k), B(4,-3), C(-9,7)are the vertices of triangle and its area is 15 sq. Unit. Find k

Ans [-3,21/13]

Question 25

The opposite vertices of a square are (-1, 2), (3, 2). Find the coordinates of other two vertices.

Question 24

If A(1,k), B(4,-3), C(-9,7)are the vertices of triangle and its area is 15 sq. Unit. Find k

Ans [-3,21/13]

Question 25

The opposite vertices of a square are (-1, 2), (3, 2). Find the coordinates of other two vertices.

Ans [(1,4),(1,0)]

Question 26

If the line joining the points (2, 1) & (5, -8) is trisected by the points P & Q. If point P lie on the line 2x - y + k = 0 Find k.

Question 26

If the line joining the points (2, 1) & (5, -8) is trisected by the points P & Q. If point P lie on the line 2x - y + k = 0 Find k.

Ans [k = -8]

Question 27

Find the reflection (image) of the point (7,-5) in the point (-3,1)

Ans [-13,7] [Hint:- point (-3,1) is the mid -point of the point given point and the reflection]

Question 28

Find the ratio in which the point (-3,k)divides the line segment joining the points (-5,-4) & (-2,3). Hence find the value of k

Question 27

Find the reflection (image) of the point (7,-5) in the point (-3,1)

Ans [-13,7] [Hint:- point (-3,1) is the mid -point of the point given point and the reflection]

Question 28

Find the ratio in which the point (-3,k)divides the line segment joining the points (-5,-4) & (-2,3). Hence find the value of k

Ans [2:1, k = 2/3]

Question 29

If (-2,2), (x,8) & (6,y) are three concyclic points whose centre is (2,5). Find x and y.

Ans [x = 6,-2, y = 8, 2]

Question 30

Find the value of k if P(2,4) is equidistant from the points A(5, k) & B(k,7)

Question 29

If (-2,2), (x,8) & (6,y) are three concyclic points whose centre is (2,5). Find x and y.

Ans [x = 6,-2, y = 8, 2]

Question 30

Find the value of k if P(2,4) is equidistant from the points A(5, k) & B(k,7)

Ans [k = 3]

Question 31

Show that the point p(-4, 2) lies on the line segment joining the points A(-4,6) & B(-4,-6)

Question 32

The points A(2, 9), B(a, 5), C(5, 5)are the vertices of a right angled triangle at B. Find a and the area of triangle ABC

Ans [a = 2, Area = 6cm

^{2}]Question 33

Find the centre of the circle passing through the points (6, -6), (3, -7) & (3, 3)

Question 34

Prove that the points P(a, b+ c),Q(b, c+ a), R(c, a+ b) are collinear.

Question 35

Find a relation between x and y if the points (2,1),(x, y) and (7,5) are collinear.

Find the centre of the circle passing through the points (6, -6), (3, -7) & (3, 3)

Question 34

Prove that the points P(a, b+ c),Q(b, c+ a), R(c, a+ b) are collinear.

Question 35

Find a relation between x and y if the points (2,1),(x, y) and (7,5) are collinear.

Ans [4x - 5y = 3]

Question 36

Find the point on the y –axis which is equidistant from the points (5,-2) & (-3,2).

Question 36

Find the point on the y –axis which is equidistant from the points (5,-2) & (-3,2).

Ans [(0,-2)]

Question 37

The centre of the circle is (2a-1,7) and is passes through the points (-3,-1). If the diameter of the circle is 20cm. Find the value of a.

The centre of the circle is (2a-1,7) and is passes through the points (-3,-1). If the diameter of the circle is 20cm. Find the value of a.

Ans [a = -4,2]

Question 38

The mid point of the sides of a triangle are (5,4),(4,6) and (5,7).Find the coordinates of the vertices of the triangle

Question 38

The mid point of the sides of a triangle are (5,4),(4,6) and (5,7).Find the coordinates of the vertices of the triangle

Ans [(4, 3), (6, 5), (4, 9)]

Question 39

In what ratio the line segment joining the points (-2,-3) & (3,7) divided by the y-axis. Also find the coordinates of the point of division.

Ans [2:3, (0,1)]

Question 40

Find the coordinates of the point equidistant from the points A(-2,-3), B(-1,0), C(7,-6)

Ans [3,-3]

Question 39

In what ratio the line segment joining the points (-2,-3) & (3,7) divided by the y-axis. Also find the coordinates of the point of division.

Ans [2:3, (0,1)]

Question 40

Find the coordinates of the point equidistant from the points A(-2,-3), B(-1,0), C(7,-6)

Ans [3,-3]

Question 41

Two vertices of a triangle ABC are given by A(6,4) & B(-2,2) and its centroid is (3,4). Find the coordinates of the third vertex C of triangle ABC.

Ans [56]

Ans [56]

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