Exploring Line Reflections in the Coordinate Plane

Interact with the following app for a few minutes. Be sure to drag point B, point C, 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.

The dashed line is called a LINE OF REFLECTION. Here, we're reflecting Lisa's pic about the line. Position the line so it coincides (lies on top of) the xAxis.

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 (a, b) is reflected about the xAxis. What would the coordinates of its image be? Express in terms of a and b.

Now move the line so that the yAxis now becomes the line of reflection.

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 (a, b) is reflected about the yAxis. What would the coordinates of its image be? Express in terms of a and b.

Is it possible to move objects around so that Lisa's image lies perfectly on top of the her original (premiage)? Try it!

Is it possible to move objects around so that Lisa's image lies perfectly on top of the her original (premiage)? Try again to see if this is possible here. Create a different pic different from what you have above.

From what you've seen, what causes Lisa's image to coincide (lie right on top of) her original image (preimage)? Describe.