Show that the four points $(1 ,2), (3,0), (7,4)$ and $(5,6)$ taken in order are the angular points of a rectangle.

Determine the ratio in which the point $(10, m)$ divides the join of $A(5, 2)$and $B(17, 14)$. Also, find the value of $m$.

Find the centroid of $∆ABC$ whose vertices are $A(-1, 0), B(5, -2)$ and $C(8, 2)$

Three vertices of a rectangle are the points $(3, 4)$, $(-1, 2)$ and $(2, -4)$; what are the co- ordinates of the fourth vertex.