Question

A parallelogram has vertices A(0,4), B(2, 2), C(4,4),

Answer 1

Answer:

yes, parallelogram ABCD is a square.

Step-by-step explanation:

Given information: ABCD is parallelogram with vertices A(0,4), B(2, 2), C(4,4), and D(2,6).

We need to check whether this parallelogram is a square or not.

The opposite side of a parallelogram are parallel and congruent. If the interior angles a parallelogram are right angles then the parallelogram is square.

Formula for slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Now, find the slopes of each side.

$m_{AB}=\dfrac{2-4}{2-0}=-1$

$m_{BC}=\dfrac{4-2}{4-2}=1$

$m_{CD}=\dfrac{6-4}{2-4}=-1$

$m_{AD}=\dfrac{6-4}{2-0}=1$

The product of slopes of two perpendicular line is -1.

The product of slopes of any two consecutive sides is -1. It means all interior angles are right angle.

Therefore, the parallelogram ABCD is a square.