English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:

A(4, 5) B(7, 6), C (4, 3), D(1, 2)

Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3,5).

Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus.
Also, find its area.

In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A(3, 1), B(6, 4), and C(8, 6). Do you think they are seated in a line?

Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).

Find the coordinates of the point which divides the line segment joining (−1,3) and (4, −7) internally in the ratio 3 : 4

Find the points of trisection of the line segment joining the points:

5, −6 and (−7, 5),

Find the points of trisection of the line segment joining the points:

(3, -2) and (-3, -4)

Find the points of trisection of the line segment joining the points:

(2, -2) and (-7, 4).

Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and(1, 2) meet

Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.

Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.

The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.

Find the ratio in which the point (2, y) divides the line segment joining the points A (-2,2) and B (3, 7). Also, find the value of y.

In what ratio is the line segment joining the points (-2,-3) and (3, 7) divided by the y-axis? Also, find the coordinates of the point of division.

In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?

Determine the ratio in which the straight line x - y - 2 = 0 divides the line segment
joining (3, -1) and (8, 9).

Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by x-axis Also, find the coordinates of the point of division in each case.

Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by y-axis. Also, find the coordinates of the point of division in each case.

Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.