Copy each figure. Draw the segment that represents the distance indicated.
14. Y to WX
15. G to HJ
16. W to UV
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.
Interior designers compute
areas and volumes, work
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
5, ( 2, 4)
2, ( 1,
9, (2, 0)
experience are necessary
before a designer can take
a licensing exam.
Write a paragraph proof of Theorem 3.9.
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
these markings centered over the window, how does she know the curtain rod
will be parallel to the ceiling?
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?
In the coordinate plane, if a line has equation
c, then the distance from a point (x
) is given by
. Determine the distance from (4, 6) to the line
whose equation is 3x
Draw a diagram that represents each description.
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.
Lesson 3-6 Perpendiculars and Distance 163
(l)Lonnie Duka/Index Stock Imagery/PictureQuest, (r)Steve Chenn/CORBIS