English Medium Class 10 - CBSE Question Bank Solutions

Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).

A (3, 2) and B (−2, 1)  are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.

Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.

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

Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1), (1, 3) and (x, 8) respectively.

Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.

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

A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0)

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

A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)

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.