A map has a scale of 4 in. = 15 mi. If you measured the distance between two cities to be 19 in. on the map, how many miles would it actually be?

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