Question

Given quadrilateral RSTU, determine if each pair of sides (if any) are parallel and which are perpendicular for the coordinates of the vertices. R(1, -3), S(4, -1), T(2, 2), U(-4, -2)

Answer 1

Use slope formula. If the slopes are the same, they are parallel. If they are negative reciprocals, they are perpendicular. 
Try using two points at a time, and see if any match or are perpendicular. Good Luck!

Answer 2

Answer:  The pair of parallel sides is (RS, TU) and the pairs of perpendicular sides are (RS, ST), (TU, ST).

Step-by-step explanation:  Given that RSTU is a quadrilateral, with vertices R(1, -3), S(4, -1), T(2, 2) and U(-4, -2).

We are given to determine the pair of parallel and perpendicular sides, if any, in quadrilateral RSTU.

We know that

two straight line are parallel if their slopes are equal and they are perpendicular if the product of their slopes is -1.

The slope of a straight line having points (a, b) and (c, d) on it is given by

$m=\dfrac{d-b}{c-a}.$

So, the slopes of the sides RS, ST, TU and RS are calculated as follows :

$m_{RS}=\dfrac{-1-(-3)}{4-1}=\dfrac{-1+3}{3}=\dfrac{2}{3},\\\\\\m_{ST}=\dfrac{2-(-1)}{2-4}=\dfrac{2+1}{-2}=-\dfrac{3}{2},\\\\\\m_{TU}=\dfrac{-2-2}{-4-2}=\dfrac{-4}{-6}=\dfrac{2}{3},\\\\\\m_{RU}=\dfrac{-2-(-3)}{-4-1}=\dfrac{-2+3}{-5}=-\dfrac{1}{5}.$

We see that

$m_{RS}=m_{TU}.$

So, the sides RS and TU are parallel.

And,

$m_{RS}\times m_{ST}=m_{TU}\times m_{ST}=\dfrac{2}{3}\times\left(-\dfrac{3}{2}\right)=-1.$

So, the sides ST is perpendicular to both RS and TU.

Thus, the pair of parallel sides is (RS, TU) and the pairs of perpendicular sides are (RS, ST), (TU, ST).