Perpendicular lines

Definition

Perpendicular lines are lines that intersect at a right angle, which is 90 degrees. Their slopes are negative reciprocals of each other in the coordinate plane.

5 Must Know Facts For Your Next Test

1. Perpendicular lines intersect to form four right angles.
2. If two lines are perpendicular, the product of their slopes is -1.
3. The slope of a vertical line is undefined, and the slope of a horizontal line is 0; these two types of lines are perpendicular.
4. In the equation $Ax + By = C$, if $A_1A_2 + B_1B_2 = 0$, then the lines represented by these equations are perpendicular.
5. Perpendicularity can be used to determine orthogonality in vector spaces.

Review Questions

• What is the relationship between the slopes of two perpendicular lines?
• How do you determine if two given linear equations represent perpendicular lines?
• What angle is formed at the intersection of two perpendicular lines?

Related terms

Slope:

The measure of steepness or incline of a line, typically represented as rise over run.

Linear Equation:

An equation that forms a straight line when graphed, commonly written in the form $y = mx + b$.

Orthogonality: A concept in vector spaces where two vectors are orthogonal if their dot product is zero; this implies they meet at right angles.