Question

Prove that the points A(0,-1), B(-2,3),C(6,7) and D( 8,3) are the vertices of
rectangle ABCD

Answer 1

Answer:

We have,

A(0, −1), B(−2, 3), C(6, 7) and D(8, 3)

AB=√(−2−0)^2 +(3+1)^2

=>√4+16=2√25

BC=√(6+2)^2+(7−3)^2

=>√64+16= 4√5

CD=√(8−6)^2+(3−7)^2

=>√4+16= 2√5

DA=√(0−8)^2+(−1−3)^2

=>√64+16=4√5

∴AB=CD and BC=DA

So, ABCD is a parallelogram.

Now,

AC=√(6−0)^2+(7+1)^2

=>√36+64=10

BD=√(8+2)^2+(3−3)^2

=>√100+0=10

Diagonals are also equal and we can see that,

AC^2=AB^2+BC^2 and BD^2=AB^2+AD^2

So, ABCD is a rectangle.

I hope this is helpful for you!

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