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

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 = 

Parallel lines mean they have the same gradient
Perpendicular lines will follow the formula 
"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 = 
      = 

TU = 
      = 

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

ST = 
     = -1

RU = 
      = 

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 :)

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.