Math Assignment Class X Ch-7 | Coordinate Geometry

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

ASSIGNMENT FOR 10 STANDARD
COORDINATE GEOMETRY

Questions based on distance formula

Question 1
Find 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]

Question 3

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

Question 4

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 5 

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

Question 6

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 7

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

Question 8

Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0)and C(-2, 5)

Answer: Isosceles triangle.

Question 9

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 = 6cm²] 

Question 10

Find the coordinates of the point equidistant from the A(5, 8), B(5, -5),and C (1, -5) 

Ans [3, 3/2]

Question 11

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

Question 12

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

Question 13

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 14

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

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

Question 15

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

Ans [(0, -2)]

Questions based on the section formula and mid-point formula.

Question 16
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 17
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 18
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 19

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 20
Find the ratio in which the line segment joining the points (-10, 2), & (3, -5) is divided by y-axis 

Ans [10 : 3]

Question 21

In what ratio the line segment joining the points (3, -5) and (-1, 6) divided by the line y = x ?

Answer: 8:7

Question 22

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

Ans [a = -4, 2]

Question 23

Points A(-1,y) and B(5, 7) lie on a circle with centre O(2, -3y) such that AB is a diameter of the circle. Find the value of y. Also find the radius of the circle.

Answer: y = -1, Radius = 5

Question 24
In what ratio does the line x - y - 2 = 0 divides the line segment joining (3, -1) & (8, 9) .

Ans [2 : 3]

Question 25

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,]

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 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 28

Find the ratio in which the point (8/5,  y) divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y.

Answer: 3 : 2, y = 13/5

Question 29

Point P divides the line segment joining the points A(4, -5) and B(1, 2) in the ratio 5 : 2. Find the coordinates of point P.

Answer : (13/7, 0)

Question 30

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 31

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]

Question 32
If A(2, 1), B(3, 4), C(0, 1) are three consecutive vertices of parallelogram. Find the 4th vertex.
Ans [-1, -2]

Question 33
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 34

AD is a median of triangle ABC with vertices A(5, -6), B(6, 4) and C(0,0). Find length AD ?

Answer:  

Question 35

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 36

P(-2, 5) and Q(3, 2) are two points. Find the coordinates of the point R on line segment PQ such that PR = 2QR.

Answer: R(4/3, 3)

Question 37

Find a relation between x and y such that the points P(x, y) is equidistant from the points A(7, 1) and B(3, 5)

Answer: x - y - 2 = 0

Question 38

ABCD is a rectangle formed by the points A(-1, -1), B(-1, 6), C(3, 6) and D(3, -1). P, Q, R and S are mid-points of AB, BC, CD and DA respectively. Show that diagonals of the quadrilateral PQRS bisect each other.

Solution Hint:

Find the coordinates of P,Q,R,S by using mid point formulas.

Find the coordinates of mid points of diagonals PR and QS which are same and are equal to (1, 5/2)

As the coordinates of mid points of PR and QS both are equal ⇒ Diagonals bisects each other.

Question 39

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 40
Find the point on the y –axis which is equidistant from the points (5,-2) & (-3,2). 

Ans [(0,-2)] 

Questions based on the centroid of triangle

Question 41

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 42

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 43

Find the centroid of the triangle whose vertices are given below 

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 44

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]

Question 45

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)]

Download Pdf Form of the Assignments

QUESTIONS DELETED FROM CBSE SYLLABUS

Question 1

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 2

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

Ans [p = -1]

Question 3
Prove that the points P(a, b+ c),Q(b, c+ a), R(c, a+ b) are collinear.
Question 4
Find a relation between x and y if the points (2,1),(x, y) and (7,5) are collinear. 

Ans [4x - 5y = 3]

Question 5

If the points A(x, y), B(-5, 7) and C(-4, 5) are collinear then show that 2x + y + 3 = 0 

Question 6

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]

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