English Medium Class 10 - CBSE Question Bank Solutions

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.

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.