Given quadrilateral rstu, tell which sides (if any) are parallel and which are perpendicular for the coordinates of the vertices. r(-1,1), s(1,-2), t(4,0), u(3,3)

RS is perpendicular to ST

Explanation:
This problem can be solved using slopes (m):
1- if m1 = m2, then lines are parallel
2- if m1*m2 = -1, then lines are perpendicular
Formula to get the slope is as follows:
slope (m) = (y2-y1) / (x2-x1)

slope of RS = (-2-1) / (1--1) = -3/2
slope of ST = (0--2) / (4-1) = 2/3
slope of TU = (3-0) / (3-4) = -3
slope of RU = (3-1)/(3--1) = 1/2

Now, checking the slopes, we will find that:
slope of RS*slope of ST = -3/2 * 2/3 = -1
This means that RS is perpendicular to ST

No other relation can be established between the slopes of the other sides.

Hope this helps :)

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