If the abscissa of a point P is 2, find the ratio in which this point divides the line segment joining the points (-4, 3) and (6, 3). Also, find the co-ordinates of point P.

Find the ratio in which the line 2x + y = 4 divides the line segment joining the points P(2, -2) and Q(3, 7).

Prove that the points A(-5, 4); B(-1, -2) and C(5, 2) are the vertices of an isosceles right angled triangle. Find the co-ordinates of D so that ABCD is a square.

M is the mid-point of the line segment joining the points A(-3, 7) and B(9, -1). Find the co-ordinates of point M. Further, if R(2, 2) divides the line segment joining M and the origin in the ratio p : q, find the ratio p : q.