Question

8. 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.
(Hint: Area of rhombus =
2
x product of its diagonals)​

Answer 1

Answer:

A(−4,−7),B(−1,2),C(8,5),D(5,−4)

AB=

(−1−(−4))

2

+(2−(−7))

2

=

3

2

+9

2

=

90

=3

10

BC=

(8−(−1))

2

+(5−2)

2

=

9

2

+3

2

=

90

=3

10

CD=

(5−8)

2

+(−4−(5))

2

=

3

2

+9

2

=

90

=3

10

DA=

(−4−(5))

2

+(−7−(−4))

2

=

9

2

+3

2

=

90

=3

10

now ,

AC=

(8−(−4))

2

+(5−(−7))

2

=

(12)

2

+(12)

2

=

144

=12

2

BD=

(5−(−1))

2

+(−4−2)

2

=

6

2

+6

2

=

72

=6

2

Since , AB=CD=BC=DA,AC



=BD

so, it is rhombus.

Area of rhombus =

2

1

×12

2

×6

2

=72