English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.

Using distance formula, find which of them is correct.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:

 (−3, 5), (3, 1), (0, 3), (−1, −4)

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:

(4, 5), (7, 6), (4, 3), (1, 2)

Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.

If Q (0, 1) is equidistant from P (5, –3) and R (x, 6), find the values of x. Also, find the distances QR and PR.

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (–3, 4).

If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible value of k?

If a ≠ b ≠ 0, prove that the points (a, a²), (b, b²) (0, 0) will not be collinear.

If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y

Find the distance of a point P(x, y) from the origin.

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:

(a sin α, –b cos α) and (–a cos α, b sin 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.