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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Respuesta :

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

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

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