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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****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]

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:-

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)

**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 = 6cm**

^{2}]

**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]

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]

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 15Find the point on the y –axis which is equidistant from the points (5, -2) & (-3, 2). **

Ans [(0, -2)]

**Question 16**

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

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.

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**

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

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

**Ans [(0,-2)]**

**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)]

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

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) .

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]

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]

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]

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]

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 ?

**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]

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

**Questions based on the centroid of triangle**

**Question 40If 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, 2/3Question 41Coordinates 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 42**

Question 43Two 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 44The 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)]

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]

Ans [56]

**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]

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.

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]

(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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