Question

Show that the points (-4,-7), (-1, 2), (8,5) and (5,-4) taken in order are the
vertices of a rhombus. And find its area​

Answer 1

Step-by-step explanation:

Let the points are

A(-4,-7),B(-1,2),C(8,5),D(5,-4)

AB=√(-1)-(-4))²+(2-(-7))²

=√3²+9²

=√90

=3√10

BC=√(8-(-1))²+(5-2)²

=√9²+3²

=√90

=3√10

CD=√(5-8)²+(-4-(5))²

=√3²+9²

=√90

=3√10

DA=√(-4-(5))²+(-7-(-4))²

=√9²+3²

=√90

=3√10

now,

AC=√(8-(-4))²+(5-(-7))²

=√(12)²+(12)

=√144

=12√12

BD=√(5-(-1))²+(-4-2)²

=√6²+6²

=√72

=6√2

Since,AB=CD=BC=DA,AC≠BD

So,it is rhombus,

Area of rhombus=1/2 × 12√2 × 6√2 = 72.