Luttrell 2012
90
Name: ______________________
Date: _____
6f – Perpendicular Lines
Lines that form at right angles are said to be perpendicular or orthogonal. If one line has a slope
of m, then the other has the slope of -1/m. The product between the slopes of perpendicular lines
is alwa
y
s -1. Another wa
y
of e
x
pressing the slopes is to sa
y
the slopes are negative reciprocals of
each other.
E
x
ample 1: Determine if the line 2
x
-
y
= 5 is perpendicular to
x
+ 2
y
= 3.
Solution: The equations can be written as
y
= 2
x
- 5 and
y
= (-½)
x
+ 1.5.
Since 2(-½) = -1, the lines are perpendicular.
E
x
ample 2: Determine if the lines 2
x
- 3
y
= 5 and 6
x
+ 4
y
= 3 are perpendicular.
Solution: The equations in slope-intercept form are
y
= (
⅔)
x
-5/3 and
y
= (-6/4)
x
+ ¾.
Since -
6/4 × ⅔ = -1, the lines are perpendicular. Note: -6/4 = -3/2 which is the
negative reciprocal of ⅔.
E
x
ample 3: Write the linear equation perpendicular to 2
x
-
y
= 5 which passes through (- 4,2).
Solution: The given line has slope of 2, so the perpendicular line must have m = -½.
Substitute the point and slope into the point-slope form to get
y
- 2 = -½(
x
+ 4).
Simplif
y
into slope-intercept form,
y
= (-½)
x
, or standard form,
x
+ 2
y
= 0.
There is a pattern in the examples that make finding perpendicular lines easier. Look out!
1. Determine which of the following lines are perpendicular. Show
y
our work.
A. 3
x
- 2
y
= 5
B. 6
x
+ 9
y
= 1 C. 6
x
- 4
y
= 4 D. 9
x
+ 6
y
= 1
2. Which of the following is perpendicular to -3
x
-
y
= 4? Show work.
A.
x
+ 3
y
= 2
B. 9
x
+ 3
y
= 3
C. 3
x
-
y
= 3
D.
x
- 3
y
= 5
3. Write the linear equation perpendicular to 5
x
- 3
y
= 1 that passes through (4, 2).
4. Write the linear equation in standard form that is perpendicular to 4
x
- 3
y
= 7 at (1,-1).
