Perpendicular lines form a right angle. The product of their slopes is –1.
Verify that the following lines are perpendicular.
Solution: Find the slopes of each line.
To verify that the lines are perpendicular, the product of their slopes must equal –1.
Determine whether the two lines are parallel, perpendicular, or neither:
Solution: Begin by finding the slopes of lines 1 and 2.
The slope of the first line is 2.
The slope of the second line is –2.
These slopes are not identical, so these lines are not parallel.
Lines 1 and 2 are neither parallel nor perpendicular.
Writing Equations of Perpendicular Lines
Writing equations of perpendicular lines is slightly more difficult than writing parallel line equations. The reason is because you must find the slope of the perpendicular line before you can proceed with writing an equation.
You now have the slope and a point. Use point-slope form to write its equation.
Multimedia Link: For more help with writing lines, visit AlgebraLab.
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Equations of Parallel and Perpendicular Lines (9:13)
- Define perpendicular lines.
- What is true about the slopes of perpendicular lines?
Determine the slope of a line perpendicular to each line given.
In 8 – 14, determine whether the lines are parallel, perpendicular, or neither.
Line a: passing through points (–1, 4) and (2, 6); Line b: passing through points (2, –3) and (8, 1).
Line a: passing through points (4, –3) and (–8, 0); Line b: passing through points (–1, –1) and (–2, 6).
Line a: passing through points (–3, 14) and (1, –2); Line b: passing through points (0, –3) and (–2, 5).
Line a: passing through points (3, 3) and (–6, –3); Line b: passing through points (2, –8) and (–6, 4).
- Line 1: 4y+x=8; Line 2: 12y+3x=1
- Line 1: 5y+3x+1; Line 2: 6y+10x=−3
- Line 1: 2y−3x+5=0; Line 2: y+6x=−3
For the following equations, find the line perpendicular to it through the given point.