Perpendicular Lines

Perpendicular lines are two lines that intersect at a 90-degree angle. This means that the slope of one line is the negative reciprocal of the other line. In other words, if the slope of one line is m, then the slope of the other line is -1/m.

Properties of Perpendicular Lines

1. Two perpendicular lines have slopes that are negative reciprocals of each other.
2. When two lines are perpendicular, their slopes multiply to -1.
3. Perpendicular lines form right angles where they intersect.

Examples of Perpendicular Lines

Here are some examples of perpendicular lines:

• Vertical lines are always perpendicular to horizontal lines.
• The x-axis is perpendicular to the y-axis in a Cartesian coordinate system.
• Two lines with slopes of 2 and -1/2 are perpendicular to each other.

How to Determine if Two Lines are Perpendicular

To determine if two lines are perpendicular, you can calculate the slopes of the lines and check if they are negative reciprocals of each other. If the product of the slopes is -1, then the lines are perpendicular.

Study Guide

Here are some key points to remember about perpendicular lines:

1. Perpendicular lines intersect at a 90-degree angle.
2. The slopes of perpendicular lines are negative reciprocals of each other.
3. The product of the slopes of perpendicular lines is -1.
4. Vertical lines are always perpendicular to horizontal lines.

Practice identifying perpendicular lines and calculating their slopes to reinforce your understanding of this concept.