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Copy each figure. Draw the segment that represents the distance indicated.

14. Y to WX

15. G to HJ

16. W to UV

R

M

G

W

X

S

Q

T

L

H

X

Z

Y

U

W

K

J

V

COORDINATE GEOMETRY

Construct a line perpendicular to through P.

Then find the distance from P to .

17. Line contains points ( 3, 0) and (3, 0). Point P has coordinates (4, 3).

18. Line contains points (0,

2) and (1, 3). Point P has coordinates ( 4, 4).

Find the distance between each pair of parallel lines.

19. y

3

20. x

4

21. y

2x

2

Interior Designer

y

1

x

2

y

2x

3

Interior designers compute

3

22. y

4x

23. y

2x

3

24. y

x

1

areas and volumes, work

4

y

4x

17

2x

y

4

3x

4y

20

with scale models, and

create budgets, in addition

to being artistic. Usually

Graph each line. Construct a perpendicular segment through the given point.

two years of college and

Then find the distance from the point to the line.

two years of practical

25. y

5, ( 2, 4)

26. y

2x

2, ( 1,

5)

27. 2x

3y

9, (2, 0)

experience are necessary

before a designer can take

a licensing exam.

28.

Write a paragraph proof of Theorem 3.9.

PROOF

Online Research

INTERIOR DESIGN

29.

Theresa is installing a curtain rod on the wall above the

For information about

window. In order to ensure that the rod is parallel to the ceiling, she measures

a career as an interior

and marks 9 inches below the ceiling in several places. If she installs the rod at

designer, visit:

these markings centered over the window, how does she know the curtain rod

will be parallel to the ceiling?

com/careers

CONSTRUCTION

30.

When framing a wall during a construction

project, carpenters often use a plumb line. A plumb line is a string

with a weight called a plumb bob attached on one end. The plumb

line is suspended from a point and then used to ensure that wall

studs are vertical. How does the plumb line help to find the

distance from a point to the floor?

ALGEBRA

31.

In the coordinate plane, if a line has equation

ax

by

c, then the distance from a point (x

, y

) is given by

1

1

ax

c

by

1

1

. Determine the distance from (4, 6) to the line

2

2

a

b

whose equation is 3x

4y

6.

CRITICAL THINKING

Draw a diagram that represents each description.

32.

a. Point P is equidistant from two parallel lines.

b. Point P is equidistant from two intersecting lines.

c. Point P is equidistant from two parallel planes.

d. Point P is equidistant from two intersecting planes.

e. A line is equidistant from two parallel planes.

f. A plane is equidistant from two other planes that are parallel.

com/self_check_quiz

Lesson 3-6 Perpendiculars and Distance 163

(l)Lonnie Duka/Index Stock Imagery/PictureQuest, (r)Steve Chenn/CORBIS

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Parent category: Education