Question

Show that four points (0, -1), (6, 7), (-2, 3) and (8, 3) are vertices of a rectangle.

Answer 1

Let A(0,−1),B(−2,3),C(6,7)andD(8,3)

AB= (−2−0) 2 +(3+1) 2

= 4+16

= 20

BC= (6+2) 2 +(7−3) 2

= 64+16

= 80

CD= (8−6) 2 +(3−7) 2

= 4+16

= 20

DA= (8−0) 2 +(3+1) 2

= 64+16

= 80

Diagonals,

AC= (6−0) 2 +(7+1) 2

= 36+64

= 100

=10

BD=(8+2) 2 +(3−3) 2

= 100+0

= 100

=10

Now we can see that opposite sides are equal

AB=CD and BC=AD units.

Also the diagonals are equal.

This means, the points are the vertices of a rectangle