English Medium कक्षा १० - CBSE Question Bank Solutions

Find the distance between the following pairs of points:

(−5, 7), (−1, 3)

Find the distance between the following pairs of points:

(a, b), (−a, −b)

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.

Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.

Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.

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 distance 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 values 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

What is the HCF of the smallest prime number and the smallest composite number?

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

Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.

A merchant has 120 liters of oil of one kind, 180 liters of another kind and 240 liters of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?