Question

Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus. Also, find its area.

Answer 1

Let the given vertices be  A(3, 0), B(4, 5), c(-1, 4) and D(-2, -1)

Here all sides of the quadrilateral ABCD are off same lengths but the diagonals are of different lengths.

So, ABCD is a rhombus.

Therefore area of rhombus ABCD=(1/2)x4√2x6√2

=24 sq. units