What if you wanted to figure out if two lines in a shape met at right angles? How could you do this? After completing this Concept, you'll be able to use slope to help you determine whether or not lines are perpendicular.
Watch the portion of this video that deals with Perpendicular Lines
Recall that the definition of
is two lines that intersect at a
If we take a closer look at these two lines, we see that the slope of one is -4 and the other is
Find the slope of the perpendicular lines to the lines below.
We are only concerned with the slope for each of these.
c) Because there is no number in front of
Find the equation of the line that is perpendicular to
First, the slope is the reciprocal and opposite sign of
First, we have to change each equation into slope-intercept form. In other words, we need to solve each equation for
Now that the lines are in slope-intercept form (also called
Watch this video for help with the Examples above.
Two lines in the coordinate plane with slopes that are opposite signs and reciprocals of each other are
and intersect at a
1. Determine which of the following pairs of lines are perpendicular.
2. Find the equation of the line that is perpendicular to the line
3. Give an example of a line that is perpendicular to the line
1. Two lines are perpendicular if their slopes are opposite reciprocals. The only pairs of lines this is true for is the
2. The perpendicular line goes through (2, -2), but the slope is
The equation is
3. Any line perpendicular to
Determine which of the following pairs of lines are perpendicular.
Determine the equation of the line that is perpendicular to the given line, through the given point.
y=x−1; (−6, 2)
y=3x+4; (9, −7)
5x−2y=6; (5, 5)
y=4; (−1, 3)
x=−3; (1, 8)
x−3y=11; (0, 13)
Determine if each pair of lines is perpendicular or not.
For the line and point below, find a perpendicular line, through the given point.