A(2, 5), B(-1, 2) and C(5, 8) are the vertices of a triangle ABC, 'M' is a point on AB such that AM : MB = 1 : 2. Find the coordinates of 'M'. Hence, find the equation of the line passing through C and M.

Three vertices of a parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2) find :

(i) the coordinates of the fourth vertex D.

(ii) length of diagonal BD.

(iii) equation of side AB of the parallelogram ABCD.

Find the equation of the line passing through the point (1, 4) and intersecting the line x - 2y - 11 = 0 on the y-axis.

A and B are the two points on the x-axis and y-axis respectively. P(2, -3) is the mid-point of AB.

Find :

(i) the coordinates of A and B.

(ii) the slope of the line AB.

(iii) the equation of the line AB.