Question

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order
Chow that the points (-4,-7), (-1,2), (8,5) and (5,-4) taken in
are the vertices of a chombus. Find its area.
2​

Answer 1

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)²

= 2✓144

BD=✓ (5−(−1))² +(−4−2)²

= ✓6²+6²

= ✓72

Since , AB=CD=BC=DA,AC=BD

so, it is rhombus.

Area of rhombus =

1/2 ×12✓2×6✓2

=72unit sq.