# Parallel And Perpendicular Lines Worksheet Page 37

Construct a Perpendicular Segment
Example
Example
2
2
COORDINATE GEOMETRY
Line contains points ( 6,
9) and (0,
1).
Construct a line perpendicular to line through P( 7,
2) not on .
Then find the distance from P to .
Graph line
and point P. Place the compass
y
1
1
4
point at point P. Make the setting wide enough
so that when an arc is drawn, it intersects in two
O
x
P
places. Label these points of intersection A and B.
-10
-4
(0, 1)
B
A
-8
( 6, 9)
Put the compass at point A and draw an arc
2
2
y
4
below line . (Hint: Any compass setting
1
O
greater than
AB will work.)
2
x
P
-10
-4
(0, 1)
B
A
-8
( 6, 9)
Using the same compass setting, put the
y
3
3
4
compass at point B and draw an arc to
intersect the one drawn in step 2. Label
O
x
P
(0, 1)
the point of intersection Q.
-10
-4
B
Study Tip
Distance
Q
A
-8
Note that the distance
( 6, 9)
from a point to the x-axis
can be determined
by looking at the
Draw PQ. PQ
. Label point R at the intersection
y-coordinate and the
4
4
y
4
distance from a point
of PQ and .
Use the slopes of PQ and
to verify
to the y-axis can be
O
that the lines are perpendicular.
determined by looking
x
P
(0, 1)
-10
-4
B
The segment constructed from point P( 7,
2)
at the x-coordinate.
R
perpendicular to the line , appears to intersect
Q
line at R( 3,
5). Use the Distance Formula
A
-8
to find the distance between point P and line .
( 6, 9)
2
2
d
(x
x
)
(y
y
)
2
1
2
1
2
2
( 7
( 3))
( 2
( 5))
25 or 5
The distance between P and is 5 units.
DISTANCE BETWEEN PARALLEL LINES
Two lines in a plane are parallel if they are everywhere
A
B
C
D E
equidistant
. Equidistant means that the distance
between two lines measured along a perpendicular line
to the lines is always the same. The distance between
K
J
H
G
F
parallel lines is the length of the perpendicular segment
AK
BJ
CH
DG
EF
with endpoints that lie on each of the two lines.
160 Chapter 3 Parallel and Perpendicular Lines