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(0, 0), S(6, 3), T(5, 5), U(-1, 2)

Answer 1

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! :)