Geometry
3.7 Perpendicular Lines in
the Coordinate Plane
Goals
Use slope to identify perpendicular lines
in a coordinate plane.
 Write equations of perpendicular lines.

April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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Review
Lines are parallel if they have the same
slope.
 Slope is rise/run.
 Lines with a positive slope rise to the
right.
 Lines with a negative slope rise to the
left.
 Horizontal Lines: slope = 0.
 Vertical Lines: slope is undefined (or
none). Geometry 3.7 Perpendicular Lines in the Coordinate Plane
3

April 10, 2015
Problem Slopes
Find the slope of the line containing (4, 6)
and (2, 6).
Do it graphically:
m 
66
42

0
0
2
Horizontal Lines have the
form y = c.
April 10, 2015
(2, 6)
(4, 6)
y=6
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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Problem Slope
Find the slope of the line containing (4, 6)
and (4, 3).
Do it graphically:
m 
63
44

3

0
undefined (no SlopE)
vertical Lines have the form
x = c.
April 10, 2015
(4, 6)
(4, 3)
x=4
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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Postulate 18
Two lines are perpendicular iff the product
of their slopes is –1.
Algebraically: m1 • m2 = –1
A vertical and a horizontal line are
perpendicular.
April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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Example
m1
1
m1 
2
2
m2  2
1
-1
m1  m 2 
2
1
2
  2    1
m1  m2
m2
April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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You don’t need a picture.
Line A contains (2, 7) and (4, 13).
Line B contains (3, 0) and (6, -1).
Are the lines perpendicular?
mA 
13  7
42

6
3
2
 1
(3)     1
 3
April 10, 2015
mB 
1 0
63

1
3
YES!
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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Exception
Slope of m1 is ?
 Undefined
m1
Slope of m2 is ?
(2, 2)
m2
(-2, 1)
(3, 1)
(2, -1)
 Zero
m1  m2  –1.
But m1  m2!
A vertical line and a
horizontal line are
perpendicular.
April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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Another way to think of it:
Two lines are perpendicular if one slope is the negative
reciprocal of the other.
3
5
 
5
3
8
1
8
1
 9
9
April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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Slope Intercept form review
y = mx + b
 m is the slope
 b is the y-intercept
 The y-intercept is at (0, b)
 Lines are parallel if they have the same
slope. They are perpendicular if the
product of their slopes is –1.

April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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More challenging problem
p1 :  3 x  2 y  2
p2 :
2 x  3 y  2
These equations are in General Form
Ax + By = C
Slope is always: 
A
B
April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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Why is this so?
Consider the equation:
8x – 4y = 12
Move the 8x:
– 4y = – 8x + 12
Divide by –4:
y = 2x – 3
Slope is?
2
Now use –A/B:
-8/(-4) = 2
April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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For –3x + 2y = 2, slope is 
For 2x + 3y = –2, slope is 
A

B
A
B
3
2


3
2
2
3
The slopes are negative reciprocals, so
the lines are perpendicular.
April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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In summary
Two lines are parallel if they have the
same slope.
 Two lines are perpendicular if the
product of their slopes is –1.
 General form is Ax + By = C and the
slope in this form is –A/B.

April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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Homework
April 10, 2015
Geometry 3.7 Perpendicular Lines in the Coordinate Plane
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