English Medium कक्षा १० - CBSE Question Bank Solutions

Find the distance between the following pair of points:

(-6, 7) and (-1, -5)

Find the distance between the following pair of points:

 (a+b, b+c) and (a-b, c-b)

Find the distance between the following pair of points:

(asinα, −bcosα) and (−acos α, bsin α)

Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`

If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y = 0.

Find the values of x, y if the distances of the point (x, y) from (-3, 0)  as well as from (3, 0) are 4.

The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.

Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.

Prove that the points A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.

An equilateral triangle has two vertices at the points (3, 4) and (−2, 3), find the coordinates of the third vertex.

Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.

Find the circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).

If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.

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

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

If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.

Find the zeros of the polynomial `f(x) = x^2 + 7x + 12` and verify the relation between its zeroes and coefficients.

Find the zeroes of the polynomial `f(x) = x^2 ˗ 2x ˗ 8` and verify the relation between its zeroes and coefficients

Find the zeroes of the quadratic polynomial `f(x) = x^2 + 3x ˗ 10` and verify the relation between its zeroes and coefficients. 

Find the zeroes of the quadratic polynomial `f(x) = 5x^2 ˗ 4 ˗ 8x` and verify the relationship between the zeroes and coefficients of the given polynomial.