EXAMPLE 4 Find the distance between two parallel lines

SCULPTURE: The sculpture on the right is drawn on a graph where units are measured in inches. What is the approximate length of SR, the depth of a seat?

EXAMPLE 4 Find the distance between two parallel lines

SOLUTION

You need to find the length of a perpendicular segment from a back leg to a front leg on one side of the chair.

The length of SR is about 18.0 inches.

The segment SR is perpendicular to the leg so the distance SR is

(35 – 50)2 + (120 – 110)2 18.0 inches.d =

The segment SR has a slope of 120 – 110 = 1015 35 – 50

– = 2–3

.

Using the points P(30, 80) and R(50, 110), the slope of each leg is 110 – 80 = 30

20 50 – 30= 3

2.

GUIDED PRACTICE for Example 4

Use the graph at the right for Exercises 5 and 6.

5. What is the distance from point A to line c?

6. What is the distance from line c to line d?

5. about 1.36. about 2.2

ANSWER

GUIDED PRACTICE for Example 4

7. Graph the line y = x + 1. What point on the line is the shortest distance from the point (4, 1). What is the distance? Round to the nearest tenth.

(2, 3); 2.8

ANSWER