Question

Show that points A(3,0) B(4,5) C (-1,4) D (-2,-2) are the sides of a rhombus

Answer 1

Answer:

Let the points of rhombus are A(3,0), B(4,5), C(-1,4) and D(-2,-1).

We know that all the sides of a rhombus are Equal.

So by distance formula we have,

Distance between two points =

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

AB=

(4−3)

2

+(5−0)

2

=

1+25

=

26

BC=

(−1−4)

2

+(4−5)

2

=

25+1

=

26

CD=

(−2+1)

2

+(−1−4)

2

=

1+25

=

26

AD=

(3−2)

2

+(0−1)

2

=

25+1

=

26

∴AB=BC=CD=AD=

26

∴ABCD is a rhombus (Proved)

AC and BD are the diagonals of the rhombus ABCD

AC=

(3−(−1))

2

+(0−4)

2

=

16+16

=

32

BD=

(4−(−2))

2

+(5−(−1))

2

=

36+36

=

72

Area= 0.5×(AC)×(BD)

Area = 0.5×

3

2×

7

2=24 Sq. units