In what ratio does the point P(a, 2) divide the line segment joining the points A(5, -3) and B(-9, 4) ? Also, find the value of 'a'.

Find the point on the y-axis whose distances from the points (3, 2) and (-1, 1.5) are in the ratio 2 : 1.

If a, b, c are in A.P., show that : (b + c), (c + a) and (a + b) are also in A.P.