polygon QRST has vertices Q41/2 , 2 R 8/2 ,2 S 8 1/2 , -3 1/2 and T 4 1/2,-3 1/2 is polygon qrst a reactangle? justify your anwerer

QRST is a rectangle.

Step-by-step explanation:

To decide whether this is a rectangle or not, we have the following options to choose from:

Prove that:

2 pairs of sides are parallel and one angle is 90°

2 pairs of opposite sides are equal and one angle is 90°

1 pair of sides is parallel and equal and one angle is 90°

All four angles are 90°

The diagonals are equal and bisect each other. (same midpoint)

I will go with option 1, because this only requires finding the slope of each of the 4 lines.

Note that:

points Q and R have the same

y

value

⇔

horizontal line

points S and T have the same

y

value

⇔

horizontal line

points Q and T have the same

x

value

⇔

vertical line

points R and S have the same

x

value

⇔

vertical line

Therefore QRST has to be a rectangle because horizontal and vertical lines meet at 90°.

The opposite sides are therefore parallel and equal and the angles are 90°

The anwser is that a

QRST  is a rectangle

a) 32pie square meters

step-by-step explanation: