CK-12 Geometry Concepts

3.9. Perpendicular Lines in the Coordinate Plane http://www.ck12.org

a)m=2, som⊥is the reciprocal and negative,m⊥=−^12.

b)m=−^23 , take the reciprocal and make the slope positive,m⊥=^32.

c) Because there is no number in front ofx, the slope is 1. The reciprocal of 1 is 1, so the only thing to do is make it
negative,m⊥=−1.

Example B

Find the equation of the line that is perpendicular toy=−^13 x+4 and passes through (9, -5).

First, the slope is the reciprocal and opposite sign of−^13. So,m=3. Now, we need to find they−intercept. 4 is
they−intercept of the given line,not our new line. We need to plug in 9 forxand -5 foryto solve for thenew
y−intercept(b).

− 5 = 3 ( 9 )+b

− 5 = 27 +b Therefore, the equation of line isy= 3 x− 32.

− 32 =b

Example C

Graph 3x− 4 y=8 and 4x+ 3 y=15. Determine if they are perpendicular.

First, we have to change each equation into slope-intercept form. In other words, we need to solve each equation for
y.

3 x− 4 y= 8 4 x+ 3 y= 15

− 4 y=− 3 x+ 8 3 y=− 4 x+ 15

y=

3

4

x− 2 y=−

4

3

x+ 5

Now that the lines are in slope-intercept form (also calledy−intercept form), we can tell they are perpendicular
because their slopes are opposite reciprocals.

Watch this video for help with the Examples above.

MEDIA

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CK-12 Foundation: Chapter3PerpendicularLinesintheCordinatePlaneB

Vocabulary

Two lines in the coordinate plane with slopes that are opposite signs and reciprocals of each other areperpendicular
and intersect at a 90◦, or right, angle.Slopemeasures the steepness of a line.