Question

The points (0, -1), (-2 ,3), (6, 7) and (8, 3) are

• A. Collinear
• B. vertices of a parallelogram which is not a rectangle
• C. Vertices of a rectangle, which is not a square
• D. None of these

Answer 1

The correct option is C Vertices of a rectangle, which is not a square

Let $A(0,-1),B(-2,3),C(6,7)andD(8,3)$

$AB=\sqrt{{(-2-0)}^2+{(3+1)}^2}=\sqrt{4+16}=\sqrt{20}$
$BC=\sqrt{{(6+2)}^2+{(7-3)}^2}=\sqrt{64+16}=\sqrt{80}$
$CD=\sqrt{{(8-6)}^2+{(3-7)}^2}=\sqrt{4+16}=\sqrt{20}$
$DA=\sqrt{{(8-0)}^2+{(3+1)}^2}=\sqrt{64+16}=\sqrt{80}$
Diagonals,

$AC=\sqrt{{(6-0)}^2+{(7+1)}^2}=\sqrt{36+64}=\sqrt{100}=10$
$BD=\sqrt{{(8+2)}^2+{(3-3)}^2}=\sqrt{100+0}=\sqrt{100}=10$
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.