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Parallel and Perpendicular Lines Exploration

Author:jamesweber, Crawfoer, Mrs_Leifer

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 PARALLEL line goes through. 3. Move point A as you wish; this will be the point that your PERPENDICULAR line goes through. 3. Click Show Parallel or Show Perpendicular options in the bottom right, as needed.

Parallel Line Exploration

Answer the following Questions

1. Plot the red line through the points (1,3) and (-2,4). What is the slope of the red line?

Check my answer

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?

Perpendicular Line Exploration

Answer the following questions.

1. Plot the red line through the points (-2,2) and (1,4). What is the slope of the red line?

Check my answer

2. Does your red line have a positive or negative slope?

Select all that apply
  • A
  • B
Check my answer (3)

3. Move A to any point. Select "Show Perpendicular". What is the slope of the new line?

Unselect "Show Perpendicular"

4. Move point A to another point of your choice. Again select "Show Perpendicular". What is the slope of the new line?

5. Repeat steps 3 and 4 for a few more movements of A. What do you notice about each of the slopes of the lines through A?

6. Move the red line to go through the points (-2,3) and (1,-1). What is the slope of the red line?

Check my answer

7. Does your red line have a positive or negative slope?

Select all that apply
  • A
  • B
Check my answer (3)

8. Select "Show Perpendicular". What is the slope of the new line?

9. Does your red line have a positive or negative slope?

Select all that apply
  • A
  • B
Check my answer (3)
Unselect "Show Perpendicular"

10. Move point A to another point of your choice. Again select "Show Perpendicular". What is the slope of both lines?

11. Repeat step 10 for a few more movements of A. What do you notice about each of the slopes of the perpendicular lines?

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