Question

Points (-2, -1), (4, 0), (3, 3) and (-3, 2) are the vertices of __

Answer 1

Let points (-2,-1),(4,0),(3,3) and (3,2) be respectively denoted by A, B, C and D.

Slope of line AB = $\frac{0+1}{4+2}=\frac{1}{6}$

Slope of line CD = $\frac{2-3}{-3-3}=\frac{-1}{-6}=\frac{1}{6}$

Slope of line AB = Slope of line CD
$\Rightarrow$ AB and CD are parallel lines to each other.
Now, slope of line $BC=\frac{3-0}{3-4}=-3$
Slope of line $AD=\frac{2+1}{-3+2}=-3$
Slope of line BC =slope of line AD
$\Rightarrow$ BC and AD are parallel to each other
Mid-point of $AC=(\frac{3-2}{2},\frac{3-1}{2}),=(\frac{1}{2},1)mid-pointofBC=(\frac{4-3}{2},\frac{2+0}{2})=(\frac{1}{2},1)$
Therefore, both pairs of oppositesides of quadrilateral ABCDare parallel. And midpoint of AC and BD is same.
Hence, ABCD is a parallelogram.