English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students. 

If the poin A(0,2)  is equidistant form the points B (3, p) and  C (p ,5) find the value of p. Also, find the length of AB.

Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).

Find the points on the y-axis which is equidistant form the points A(6,5)  and B(- 4,3) 

If the points p (x , y) is point equidistant from the points A (5,1)and B ( -1,5) , Prove that 3x=2y

If  p(x , y)  is point equidistant from the points A(6, -1)  and B(2,3) A , show that x – y = 3

Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).

If the point A (4,3) and B ( x,5)  lies on a circle with the centre o (2,3) . Find the value of x.

If the point C ( - 2,3)  is equidistant form the points A (3, -1) and Bx (x ,8)  , find the value of x. Also, find the distance between BC

If the point P (2,2)  is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.

If the point ( x,y ) is equidistant form the points ( a+b,b-a ) and (a-b ,a+b ) , prove that bx = ay

Show that the following points are the vertices of a square:

(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)

Show that the following points are the vertices of a square:

A (6,2), B(2,1), C(1,5) and D(5,6)

Show that the following points are the vertices of a square:

A (0,-2), B(3,1), C(0,4) and D(-3,1)

Show that the points A(3,0), B(4,5), C(-1,4) and D(-2,-1) are the vertices of a rhombus. Find its area.

Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.

Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?

Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.

Show that the following points are the vertices of a rectangle.

A (2, -2), B(14,10), C(11,13) and D(-1,1)

Show that the following points are the vertices of a rectangle

A (0,-4), B(6,2), C(3,5) and D(-3,-1)