Find the distance of a point P(x, y) from the origin.

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.

Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10, 12). Also, find the coordinates of the point of division

Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right
triangle

If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 square units, then prove that  x + y = 15.

In fig., the area of triangle ABC (in sq. units) is

• 15

• 10

• 7.5

• 2.5

Find the ratio in which the line segment joining the points A(3,- 3) and B(- 2, 7) is divided by x-axis. Also find the coordinates of the point of division

Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.

A(4, - 6), B(3,- 2) and C(5, 2) are the vertices of a ΔABC and AD is its median. Prove that the median AD divides ΔABC into two triangles of equal areas.

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q.