Given quadrilateral rstu, determine if each pair of sides (if any) are parallel and which are perpendicular for the coordinates of the vertices. r(0, 0), s(6, 3), t(5, 5), u(-1, 2)

Before we go into this, here's the formula: (y2-y1)/(x2-x1)

Pair 1: RS TU
> Slope of RS = 2/3
> Slope of TU = 2/3
Since both slopes are they same, they are parallel.

Pair 2: RS ST
> Slope of RS = 2/3
> Slope of ST = -3/2
Since the slopes are negative reciprocals of each other, they are perpendicular. 

Same goes for the last pair, which is TU ST.
> Slope of TU = 2/3
> Slope of ST = -3/2
They're negative reciprocals, hence they are perpendicular.

Hope this helps! :)