English Medium Class 10 - CBSE Question Bank Solutions

Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.

Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.

Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.

Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area

If P and Q are two points whose coordinates are (at² ,2at) and (a/t² , 2a/t) respectively and S is the point (a, 0). Show that `\frac{1}{SP}+\frac{1}{SQ}` is independent of t.

If two vertices of an equilateral triangle be (0, 0), (3, `sqrt3`), find the third vertex using distance formula.

Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). Also, find its circum radius

If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.

Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle

If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus

Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in the following.

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

Find the distance between the following pairs of points:

(2, 3), (4, 1)

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)