Exploring Reflections
Exploring Reflections - Part 1
Click on the button that says Axis of Symmetry. [Recall that we sometimes refer to the axis of symmetry as the line of reflection.] There will be two points on the axis of symmetry that you can move around. Spend some time moving this line around. You can click on the button that says Reflect to see where the reflected image will show up.
Exploring Reflections - Part 2
Make sure the axis of symmetry (or line of reflection) is the x-axis. You can move around the original points if you would like to explore more.
In your own words, what pattern do you notice as we go from the pre-image to the image?
Coordinate notation is the function that maps the pre-image to the image. In 8th grade, we used the term algebraic representation instead of coordinate notation. Which of the following is the coordinate notation for reflecting across the x-axis?
Reflections Exploration - Part 3
Make sure the axis of symmetry is the y-axis. You can move around the original points if you would like to explore more.
In your own words, what pattern do you notice as we go from the pre-image to the image?
Which of the following is the coordinate notation for reflecting across the y-axis?
Exploring Reflections - Part 4
Make sure the axis of symmetry is the line y = x. You can move around the original points if you would like to explore more.
What patterns do you notice as we go from the pre-image to the image?
Which of the following is the coordinate notation for reflecting across the line y = x?
Exploring Reflections - Part 5
For the final part of this activity, we will work backwards. You are not able to move the reflection points, but you are still able to move the reflection line.
First, make sure that the axis of symmetry is the x-axis. A' is the image at (-3, 5). What are the coordinates of the pre-image, A?
Next, move the axis of symmetry to the y-axis. D' is the image at (7, -4). What are the coordinates of the pre-image D?
Finally, move the axis of symmetry to the line y = x. C' is the image at (-1, -6). What are the coordinates of the pre-image C?
Extension Activity
In this extension, we will see what happens when the axis of symmetry is something other than the x-axis, the y-axis, or the line y = x.
Extension 1:
Move the axis of symmetry to the line y = -2. Recall that this is a horizontal line parallel to the x-axis. Make sure that point A is on (1, 4).
How is this similar to reflecting across the x-axis? How is it different from reflecting across the x-axis? What are the coordinates of A'? Could you write the coordinate notation (or algebraic rule)?
Extension 2:
Move the axis of symmetry to the line x = 3. This is a vertical line parallel to the y-axis. Make sure that point B is at (2, 2).
How is this similar to reflecting across the y-axis?
How is this different to reflecting across the y-axis?
What are the coordinates of B'?
Extension 3:
Move the axis of symmetry to the line y = -x. Make sure that point D is at (3,1).
How is this similar to reflecting across the line y = x?
How is this different to reflecting across the line y = x?
What are the coordinates of D'?
Is there a rule for this transformation?