CK-12 Geometry Concepts

http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines

Guided Practice

1. Determine which of the following pairs of lines are perpendicular.
   
   
   • y=− 2 x+3 andy=^12 x+ 3
   
   
   • y= 4 x−2 andy= 4 x+ 5
   
   
   • y=−x+5 andy=x+ 1
   
   
   
   


2. Find the equation of the line that is perpendicular to the liney= 2 x+7 and goes through the point (2, -2).


3. Give an example of a line that is perpendicular to the liney=^23 x−4.

Answers:

1. Two lines are perpendicular if their slopes are opposite reciprocals. The only pairs of lines this is true for is the
   first−2 and^12 are opposites and reciprocals.


2. The perpendicular line goes through (2, -2), but the slope is−^12 because we need to take the opposite reciprocal
   of 2.

y=−

1

2

x+b

− 2 =−

1

2

( 2 )+b

− 2 =− 1 +b

− 1 =b

The equation isy=−^12 x−1.

3. Any line perpendicular toy=^23 x−4 will have a slope of−^32. Any equation of the formy=−^32 x+bwill work.

Practice

1. Determine which of the following pairs of lines are perpendicular.
   (a)y=− 3 x+1 andy= 3 x− 1
   (b) 2x− 3 y=6 and 3x+ 2 y= 6
   (c) 5x+ 2 y=−4 and 5x+ 2 y= 8
   (d)x− 3 y=−3 andx+ 3 y= 9
   (e)x+y=6 and 4x+ 4 y=− 16

Determine the equation of the line that isperpendicularto the given line, through the given point.

2.y=x−1;(− 6 , 2 )

3.y= 3 x+4;( 9 ,− 7 )

4. 5x− 2 y=6;( 5 , 5 )
   5.y=4;(− 1 , 3 )
   6.x=−3;( 1 , 8 )
   7.x− 3 y=11;( 0 , 13 )

Determine if each pair of lines is perpendicular or not.