Label your diagram with the following new points:
Which segment do you think would measure the distance between
point C and 𝐴𝐵? (multiple choice)
A) 𝐶𝐷
B) 𝐶𝐸
C) 𝐶𝐹
D) 𝐶𝐺
CORRECT ANSWER:
B) 𝐶𝐸
D
E
F
G
The construction of a line perpendicular to an existing line through a point not on the
existing line in Extend Lesson 1-5 establishes that there is at least one line through a
point, P, that is perpendicular to a line, 𝐴𝐵. The following postulate states that this line
is the only line through P perpendicular to 𝐴𝐵.
In other words, if you have a line,
and have a point not on the line,
then there is only one line that
exists that is perpendicular to the
original line that goes through the point.
a
W
Construct Distance From Point to a Line
A. A certain roof truss is designed so that the
center post extends from the peak of the roof
(point A) to the main beam. Construct and
name the segment whose length represents the
shortest length of wood that will be needed to
connect the peak of the roof to the main beam.
A
X
Main
Beam
ANSWER: 𝐴𝑋
The shortest length will
always be found by
using the segment that
is perpendicular
B. Which segment represents the
shortest distance from point A to DB?
ANSWER: 𝐴𝑋
The shortest length will
always be found by
using the segment that
is perpendicular
Extra Examples
1. Given triangle ABC, draw the shortest distance from A to 𝐵𝐶.
B
A
C
2. Given the pentagon, draw the shortest distance from A to 𝐶𝐷.
B
A
C
E
D
By definition, parallel lines do not intersect. An alternate definition states that two
lines in a plane are parallel if they are everywhere equidistant. Equidistant means that
the distance between two lines measured along a perpendicular line to the lines is
always the same. This leads to the definition of the distance between two parallel
lines.
2
Find the distance between each pair of
parallel lines with the given equations.
a) y = 2
y=3
b) x = 9
x=1
c) y = -5
y=7
d) x = 4
x = -6
Distance from a Point to a Line on Coordinate Plane
COORDINATE GEOMETRY
A. Line s contains points at (0,
0) and (–5, 5). Find the
distance between line s and
point
V(1, 5).
(–5, 5)
V(1, 5)
(0, 0)
COORDINATE GEOMETRY
B. Line n contains points (2, 4) and (–4, –2).
Find the distance between line n and point
B(3, 1).
Distance Between Parallel Lines
A. Find the distance between the parallel lines a and
b whose equations are y = 2x + 3 and y = 2x – 1,
respectively.
b
a
p
B. Find the distance between the parallel lines a and
b whose equations are
respectively.
and
,