Question

A carpenter is making a shelf in the shape of a parallelogram. She begins by drawing parallelogram RSTU on a coordinate plane with vertices R(1,0),S(-4,0), and T (-2,3). What are the coordinate of vertex U?

Answer 1

The coordinates would be (3, 3).

The slope from R to S is given by

m = (0 - 0)/(-4-1) = 0/-5 = 0

The distance from R to S is 5 units straight across.

This means the slope from T to U will be 0, and it will be a horizontal segment.  This means the y-coordinate of U will be 3, since the y-coordinate of T is 3.

The distance from T to U will be 5 as well; -2+5 = 3 for the x-coordinate.

This makes the point (3, 3).