Exploring Line Reflections

DIRECTIONS:

1) Position Wily Coyote (using points A and B) anywhere you'd like within the coordinate plane. 2) Select the REFLECT ABOUT LINE tool. Then drag a rectangle around points A, B, and Wily's picture. This should cause these 3 items to become highlighted. Select the dashed line. 3) The images of these items should now appear. Please answer the questions that appear below the applet.

1.

Move the ORANGE POINTS so that the dashed line lies right on top of the yAxis. What do you have as Wily's corner points ( ?, ??). Write them down below. What are the coordinates of the images of these points? Please record these below too. Do you notice anything interesting? Explain.

2.

According to your observations from (1), what would the image of any point (x, y) after being reflected about the yAxis? (Write your response in terms of x and y).

3.

Move the ORANGE POINTS so that the dashed line lies right on top of the xAxis. What do you have as Wily's corner points ( ?, ??). Write them down below. What are the coordinates of the images of these points? Please record these below too. Do you notice anything interesting? Explain.

4.

According to your observations from (1), what would the image of any point (x, y) after being reflected about the xAxis? (Write your response in terms of x and y).

5.

Move the orange points so the equation of the line becomes . What is the image of point (a, b) under a reflection about the line ?

6.

Move the 2 orange points around to change the equation of the line to . What is the image of point (a, b) under a reflection about the line ?