CPM Homework Help : INT3 Problem 4-92

What is the distance from the point $(-5,-12)$ to the line $y=-\frac{5}{3}x+8$ ?

Step 1:

Use what you know about perpendicular slopes to write the equation of a line perpendicular to
the given line through the given point.

Step 2:

Find the intersection of the two lines you now have.

Step 3:

Find the distance from this intersection point to the given point.

Partial Solution:

The equation of the perpendicular line is:

$y = \frac{3}{5}(x+5) - 12$

The lines intersect at the point $(7.5,−4.5)$ .