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 A(3,0);B(4,5);C(-1,4) and D(-2,-1)

Then being a rhombus all side are equal.(like square)

AB=BC=CD=DA

by using distance formula

AB=√26

BC=√26

CD=√26

DA=√26

But rhombus does not have equal diagonal as square

AC=6√2(d1)

BD=4√2(d2)

Area of rhombus=1/2×d1×d2

=1/2×6√2×4√2

=24 sq.units