Question

Determine whether S(–2, 3), T(–1, 4), R(4, –1), P(3, –2) is a rectangle or not. Justify your answer using Slope Formula.
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Answer 1

The side of a rectangle is perpendicular to the pair of adjacent sides.

STRP is a rectangle

The coordinates of the rectangle are:

$S = (-2,3)$

$T = (-1,4)$

$R = (4,-1)$

$P = (3,-2)$

See attachment for the rectangle

Using the attached figure as a guide

• The slopes of ST and PR must be equal
• The slopes of PS and RT must be equal

The slope is calculated as:

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

So, we have:

$m_{ST} = \frac{4-3}{-1--2} = \frac{1}{1} = 1$

$m_{PR} = \frac{-2--1}{3-4} = \frac{-1}{-1} = 1$

$m_{PS} = \frac{-2-3}{3--2} = \frac{-5}{5} = -1$

$m_{RT} = \frac{-1-4}{4--1} = \frac{-5}{5} = -1$

The first set of conditions are met, because

$m_{ST} = m_{PR} = 1$

$m_{RT} = m_{PS} = -1$

Next, the following must be true:

$m_{ST} \times m_{RT} = -1$ ---- this proves that adjacent sides are perpendicular

So, we have:

$1 \times -1= -1$

$-1= -1$

The above equation is true.

Hence, STRP is a rectangle

Read more about rectangles at:

https://brainly.com/question/2913275