Perpendicular

Definition

Perpendicular refers to a relationship between two lines, line segments, or vectors where they intersect at right angles, forming a 90-degree angle. This concept is particularly important in the context of understanding the slope-intercept form of an equation of a line and finding the equation of a line.

5 Must Know Facts For Your Next Test

1. Two lines are perpendicular if their slopes are negative reciprocals of each other, meaning the product of their slopes is -1.
2. The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope.
3. When finding the equation of a line that is perpendicular to another line, the new line's slope is the negative reciprocal of the original line's slope.
4. Perpendicular lines intersect at a 90-degree angle, forming a right angle.
5. Perpendicular lines are often used to describe the relationship between the x-axis and y-axis, as well as the relationship between the rise and run of a line.

Review Questions

• Explain how the concept of perpendicular lines is related to the slope-intercept form of an equation of a line.
  • In the slope-intercept form of an equation of a line, $y = mx + b$, the slope $m$ represents the steepness of the line. When two lines are perpendicular, their slopes are negative reciprocals of each other, meaning the product of their slopes is -1. This relationship between the slopes of perpendicular lines is crucial for understanding how to find the equation of a line that is perpendicular to another line.
• Describe the process of finding the equation of a line that is perpendicular to another line.
  • To find the equation of a line that is perpendicular to another line, you first need to know the slope of the original line. The slope of the perpendicular line will be the negative reciprocal of the original line's slope. Once you have the slope of the perpendicular line, you can use the point-slope form or the slope-intercept form to write the equation of the perpendicular line. This process is essential for tasks like finding the equation of a line that is perpendicular to a given line and passing through a specific point.
• Analyze the role of perpendicular lines in the context of the Cartesian coordinate system and the relationship between the x-axis and y-axis.
  • In the Cartesian coordinate system, the x-axis and y-axis are perpendicular to each other, intersecting at a 90-degree angle. This perpendicular relationship between the axes is fundamental to the coordinate system and allows for the unique representation of points and the calculation of distances and slopes. Understanding the concept of perpendicular lines is crucial for interpreting and working with graphs, as well as for understanding the geometric properties of the coordinate plane.

Related terms

Slope: The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line.

Angle: An angle is the measurement of the rotation between two intersecting lines or line segments, typically expressed in degrees or radians.

Intersection: The intersection of two lines, line segments, or vectors is the point at which they cross or meet.