# Exploration: Parallel and Perpendicular Lines

## Directions

In this activity, you will explore the slopes of lines that are parallel and perpendicular to a given line (in red). 1. Drag the two blue points to give you a red line. 2. Move point D as you wish; this will be the point that your second line goes through. 3. Click Show Parallel or Show Perpendicular options in the bottom right, as needed.

## Parallel Line Exploration

1. Plot the red line through the points (1,3) and (-2,4). What is the slope of the red line? 2. Move D to any point. Select "Show Parallel". What is the slope of the new line? Unselect "Show Parallel" 3. Move point D to another point of your choice. Again select "Show Parallel". What is the slope of the new line? 4. Repeat steps 2 and 3 for a few more movements of D. What do you notice about each of the slopes of the lines through D?

Describe a relationship between two parallel lines' slopes.

## Perpendicular Line Exploration

1. Plot the red line through the points (-2,2) and (1,4). What is the slope of the red line? 2. Does your red line have a positive or negative slope? 3. Move D to any point. Select "Show Perpendicular". What is the slope of the new line? Unselect "Show Perpendicular" 4. Move point D to another point of your choice. Again select "Show Perpendicular". What is the slope of the new line? 5. Repeat steps 8 and 9 for a few more movements of D. What do you notice about each of the slopes of the lines through D? 6. Move the red line to go through the points (-2,3) and (1,-1). What is the slope of the red line? 7. Does your red line have a positive or negative slope? ﻿8. Move D to any point. Select "Show Perpendicular". What is the slope of the new line? Unselect "Show Perpendicular" 9. Move point D to another point of your choice. Again select "Show Perpendicular". What is the slope of the new line? 10. Repeat steps 8 and 9 for a few more movements of D. What do you notice about each of the slopes of the lines through D?

Describe a relationship between two perpendicular lines' slopes.

Write an equation parallel to the line 3x+5=y

Write an equation perpendicular to the line 3x+5=y