English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

Prove that (4, 3), (6, 4) (5, 6) and (3, 5)  are the angular points of a square.

Prove that the points A(-4,-1), B(-2, 4), C(4, 0) and D(2, 3) are the vertices of a rectangle.

The line segment joining the points P(3, 3) and Q(6, -6) is trisected at the points A and B such that Ais nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

The points A(2, 0), B(9, 1) C(11, 6) and D(4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.

If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.

If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.

If the coordinates of the mid-points of the sides of a triangle be (3, -2), (-3, 1) and (4, -3), then find the coordinates of its vertices.

Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.

If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.

Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.

Determine the ratio in which the point P (m, 6) divides the join of A(−4, 3) and B(2, 8). Also, find the value of m.

Determine the ratio in which the point (-6, a) divides the join of A (-3, 1)  and B (-8, 9). Also, find the value of a.

The line joining the points (2, 1) and (5, −8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0. Find the value of k.

In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?

Solve the following quadratic equations by factorization: 

`(2x – 3)^2 = 49` 

`x^2-6x+3=0` 

`x^2-4x+1=0`

`x^2+8x-2=0`

`4x^2+4sqrt3x+3=0` 

`2x^2+5x-3=0`