Perpendicular Lines

We already mentioned that parallel lines have the same slope. The animation shows that the slope of a perpendicular line is the opposite reciprocal of the slope of a given line.

Example 1: 

What is the slope of a line perpendicular to that line?

 

 

 

Example 2: 

What is the slope of line AB

Solution:

The slope of the line with x-intercept 9 and y-intercept 4 is negative since it goes downhill:

Since line AB is perpendicular to this line, its slope is the opposite reciprocal:

Example 3: 

A line has equation y = 3x + 2.  What is an equation of a line perpendicular to this line, containing the point (4, 5)?

Solution:

The slope of the given line is 2 (m is the number in front of x).  As a fraction,

The perpendicular line's slope is the opposite reciprocal:

Now use the slope formula with (4, 5) for (x₁, y₁) and (x, y) for (x₂, y₂):

Multiply both sides by (x – 4) and simplify:

 

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