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Given quadrilateral RSTU, determine if each pair of sides (if any) are parallel and which are perpendicular for the coordinates of the vertices.

R(-l, -5), S(8, 2), T(5, 5), U(-4, -2)

the options are
a) parallel
b) perpendicular
c) none

Given quadrilateral RSTU, determine if each pair of sides (if any) are parallel and-example-1
User Zpete
by
8.4k points

2 Answers

1 vote
We would need to figure out the gradient of each "pair", as provided in the image.

The equation of the gradient is found by,

m =
( y_(2 ) - y_(1 ) )/( x_(2 ) - x_(1 ) )

Parallel lines mean they have the same gradient
Perpendicular lines will follow the formula
m_(1 ) * m_(2 ) = -1
"None" will apply to those that do not follow either.

Now we calculate the gradient of the pairs given to us by substituting the x and y values.

RS =
(2-5)/(8-(-1) )
=
-(1)/(3)

TU =
(-2 - 5)/(-4 -5)
=
(7)/(9)

Therefore, the "pair" RS and TU will be NONE.

ST =
(5 - 2)/(5-8)
= -1

RU =
(-2 -5)/(-4 -(-1) )
=
(7)/(3)

Therefore, the "pair" ST and RU is also NONE.

Hope this helped! Feel free to ask me if there's any part of the working you don't understand :)
User Edouard Barbier
by
8.7k points
4 votes
RS -- a) is parallel to -- TU (by same slope = 7/9)
ST -- a) is parallel to -- RU (by same slope = -1)

Therefore it is a parallelogram, not a rectangle, because there are two sets of parallel lines, but each.set is not perpendicular to the other set. 7/9 is not the negative reciprocal of -1. It would have needed to.be 7/9 and -9/7, or -1 and +1.
User Kalanamith
by
8.6k points

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