Perpendicular Lines

Definition

Perpendicular lines are two lines that intersect at a 90-degree angle, forming a perfect right angle. This geometric relationship has important implications in the context of graphing linear equations, understanding slope, and determining the equation of a line.

5 Must Know Facts For Your Next Test

1. Perpendicular lines have a slope that is the negative reciprocal of the other line's slope, meaning their slopes multiply to give -1.
2. When graphing linear equations, perpendicular lines will intersect at a 90-degree angle, forming a right angle.
3. The equation of a line perpendicular to another line can be found by taking the negative reciprocal of the original line's slope and using the same y-intercept.
4. Perpendicular lines are often used to find the shortest distance between a point and a line or between two lines.
5. Determining whether two lines are perpendicular is an important step in solving many geometry and algebra problems.

Review Questions

• How are the slopes of two perpendicular lines related?
  • The slopes of two perpendicular lines are negative reciprocals of each other. If the slope of one line is $m$, then the slope of the perpendicular line will be $-1/m$. This relationship is crucial for graphing linear equations and finding the equation of a line perpendicular to another.
• Explain how perpendicular lines are used to find the equation of a line
  • When given the equation of a line, you can use the concept of perpendicular lines to find the equation of a line that is perpendicular to the original. To do this, you first find the slope of the original line, then take the negative reciprocal of that slope to get the slope of the perpendicular line. Finally, you can use this new slope and a point on the perpendicular line to write the equation in the standard $y = mx + b$ form.
• Analyze the role of perpendicular lines in solving geometric and algebraic problems
  • Perpendicular lines are fundamental to many geometric and algebraic problems, such as finding the shortest distance between a point and a line, or between two intersecting lines. Their 90-degree angle relationship allows you to apply properties like the Pythagorean Theorem to solve for unknown values. Additionally, the slope relationship of perpendicular lines is crucial for graphing, determining the equation of a line, and analyzing the behavior of linear functions.

Related terms

Parallel Lines: Parallel lines are two or more lines that never intersect and are always the same distance apart.

Slope: Slope is a measure of the steepness or incline of a line, typically expressed as the change in y-values divided by the change in x-values.

Equation of a Line: The equation of a line represents the relationship between the x and y coordinates of points on the line, often expressed in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.