Question

Prove that a {0,0}b,{7,0}.c{7,5}and d{0,5}are the vertices of a rectangle?

Answer 1

Step-by-step explanation:

let the vertices of a parallelogram be A(4,5),B(7,6),C(6,3)D(3,2)

So by distance formula we have,

Distance between two points =

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

AB=

(7−4)

2

+(6−5)

2

=

9+1

=

10

BC=

(6−7)

2

+(3−6)

2

=

1+9

=

10

CD=

(3−6)

2

+(2−3)

2

=

9+1

=

10

AD=

(3−4)

2

+(2−5)

2

=

1+9

=

10

∴ AB=CD and BC=AD

∴ Opposite sides are equal

Hence,ABCD is a parallelogram (Proved)

Also,AB=BC=CD=AD=

10

i.e. all the sides are

equal