What you’ll learn
Use slope criterion for perpendicular lines.
Key idea
The two slopes must multiply to negative one; changing only a sign is insufficient in general.
Perpendicular finite slopes multiply to negative one; changing only sign generally fails.
Worked example
Enter the exact value or ordered values in the format requested below.
Line l passes through A=(-3, -2), B=(-1, 3). Find the exact slope of a nonvertical perpendicular line.
- Line l has finite nonzero slope 5/2.
- The perpendicular slope is -1/(5/2)=-2/5; 5/2*-2/5=-1.
Answer: -2/5
Quick Check
Evaluate a worked attempt at use slope criterion for perpendicular lines, identify the first invalid step, and provide the correction.
Line l through A=(-3, 0), B=(-2, -5) has slope -5. Student Step 1 says finite perpendicular slopes have product -1. Step 2 chooses 5 by changing sign only. Locate and repair the first invalid step.