Exploring Line Reflections in the Coordinate Plane (Ver 1)

Interact with the following app for a few minutes. Be sure to drag the LARGE POINTS, the dashed line, and Lisa's picture around!
In the app above, what do you notice? What do you wonder? Notice anything interesting? If so, describe.
Here, we are REFLECTING Lisa's pic ABOUT A LINE. Now reposition the line so it coincides (lies on top of) the X-AXIS.
In the app above, move Lisa around to get different primage points. Then, record their images in the image column.
Take a look at the table of data above. Suppose a point [b]([i]a[/i], [i]b[/i])[/b] is reflected about the xAxis. What would the coordinates of its image be? Express in terms of [b][i]a[/i] [/b]and [b][i]b[/i].[/b]
Now reposition the line so it coincides (lies on top of) the Y-AXIS.
In the app above, move Lisa around to get different primage points. Then, record their images in the image column.
Take a look at the table of data above. Suppose a point [b]([i]a[/i], [i]b[/i])[/b] is reflected about the yAxis. What would the coordinates of its image be? Express in terms of [b][i]a[/i] [/b]and [b][i]b[/i].[/b]
Is it possible to move objects around so that Lisa's image lies perfectly on top of the her original (premiage)? Try it!
From what you've seen, what causes Lisa's image to coincide (lie right on top of) her original image (preimage)? Describe.
Try again to see if it is possible to move Lisa's image on top of her preimage. Create a different setup from what you created above.
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– Tim Brzezinski

Information: Exploring Line Reflections in the Coordinate Plane (Ver 1)