Show that the points (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.

Vertices of the rhombus are: A(-3, 2), B(-5, -5), C(2, -3) and D(4, 4)

We know that diagonals of a rhombus bisect each other, therefore point of intersection of diagonals is:

Abscissa of Mid point of AC =

Ordinate of Mid point of AC =

Abscissa of Mid point of BD =

Ordinate of Mid point of BD =

Since the diagonals AC and BD bisect each other at O, therefore it is a rhombus.

Length of diagonal AC = = = = units

Length of diagonal BD = = = = units

Area of rhombus = = = 45 sq units

Area of rhombus is 45 sq units