Perpendicular lines

Definition

Perpendicular lines are two lines that intersect at a right angle (90 degrees). In the coordinate plane, their slopes are negative reciprocals of each other.

5 Must Know Facts For Your Next Test

1. If two lines are perpendicular, the product of their slopes is -1.
2. Perpendicularity in the coordinate plane can be checked using the slopes of the lines.
3. The equation of a line perpendicular to another given line can be found by taking the negative reciprocal of its slope.
4. Perpendicular lines intersect at exactly one point unless they lie on different planes.
5. In trigonometry, perpendicular vectors have a dot product equal to zero.

Review Questions

• What is the relationship between the slopes of two perpendicular lines?
• How do you determine if two lines are perpendicular in a coordinate plane?
• Given a line with slope m, what is the slope of a line perpendicular to it?

Related terms

Slope: The measure of steepness or inclination of a line, typically represented as $m$.

Right Angle: An angle that measures exactly 90 degrees.

Negative Reciprocal: $-\frac{1}{m}$ for a given slope $m$, used to determine perpendicularity.