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