The side of a rectangle is perpendicular to the pair of adjacent sides.
STRP is a rectangle
The coordinates of the rectangle are:
[tex]S = (-2,3)[/tex]
[tex]T = (-1,4)[/tex]
[tex]R = (4,-1)[/tex]
[tex]P = (3,-2)[/tex]
See attachment for the rectangle
Using the attached figure as a guide
The slope is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2-x_1}[/tex]
So, we have:
[tex]m_{ST} = \frac{4-3}{-1--2} = \frac{1}{1} = 1[/tex]
[tex]m_{PR} = \frac{-2--1}{3-4} = \frac{-1}{-1} = 1[/tex]
[tex]m_{PS} = \frac{-2-3}{3--2} = \frac{-5}{5} = -1[/tex]
[tex]m_{RT} = \frac{-1-4}{4--1} = \frac{-5}{5} = -1[/tex]
The first set of conditions are met, because
[tex]m_{ST} = m_{PR} = 1[/tex]
[tex]m_{RT} = m_{PS} = -1[/tex]
Next, the following must be true:
[tex]m_{ST} \times m_{RT} = -1[/tex] ---- this proves that adjacent sides are perpendicular
So, we have:
[tex]1 \times -1= -1[/tex]
[tex]-1= -1[/tex]
The above equation is true.
Hence, STRP is a rectangle
Read more about rectangles at:
https://brainly.com/question/2913275