Prove that the points A (0, 1), B(1, 4), C(4, 3) and D(3, 0) are the verticesof a square.

35
Show that the points A(1, 0), B(5, 3), C(2, 7) and D(-2, 4) are thevertices of a parallelogram. (Hint: Diagonals of a parallelogram bisecteach other).
36
If the distances of A(x, y) from P(a + b, b - a) and Q(a - b, a + b) are equal,prove that bx = ay.
38
Show that the points (1, 1), (-2, 7) and (3, -3) are collinear.
39
Find the ratio in which the points (2, 5) divides the line-segment joining thepoints (-1, 2) and (4, 7).