Triangle QRS has been rotated 90° to create triangle TVU. Using the image below, prove that line RS and VU have the opposite and reciprocal slopes. You must show all of your work.

The slopes are the opposite and reciprocal

Step-by-step explanation:

The Slope of a Line

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

We need to prove lines RS and VU of the figure have the opposite and reciprocal slope, i.e., the lines are perpendicular.

Finding the coordinates of the points from the image:

R=(-2,5) S=(-5,2) V=(5,2) U=(2,5)

The slope of the line RS is:

The slope of line VU is:

Since:

The slopes are the opposite and reciprocal

1.m=2

2.m=-6

3.m=3

4.m=1/2

glad to