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(-1, -5), S(8, 2), T(5, 5), U(-4, -2)

Answer 1

RS and TU are parallel to each other.

ST and UR are parallel to each other.

Explanation:

Answer 2

The sides are parallel if they have the same slope.

RS slope = (2+5)/(8+1)
= 7/9

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

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

UR slope = (-2+5)/(-4+1)
= -1

It's a parallelogram.
RS and TU are parallel to each other.
ST and UR are parallel to each other.