Perpendicular

Definition

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

5 Must Know Facts For Your Next Test

1. Two lines are perpendicular if and only if the product of their slopes is -1.
2. If one line has a slope of $m$, the perpendicular line will have a slope of $-\frac{1}{m}$.
3. The equation of a line perpendicular to $y = mx + b$ and passing through point $(x_1, y_1)$ is given by $y - y_1 = -\frac{1}{m}(x - x_1)$.
4. In coordinate geometry, the x-axis and y-axis are perpendicular to each other.
5. In three-dimensional space, vectors are perpendicular if their dot product is zero.

Review Questions

• What is the relationship between the slopes of two perpendicular lines?
• How do you find the equation of a line that is perpendicular to another given line and passes through a specific point?
• If a line has a slope of $2$, what is the slope of a line perpendicular to it?

Related terms

Slope: The measure of the steepness or incline of a line, often denoted as $m$ in equations.

Right Angle: An angle that measures exactly 90 degrees.

Negative Reciprocal: The inverse value with an opposite sign; for example, the negative reciprocal of $a$ is $-\frac{1}{a}$.