# Exploring Line Reflections in the Coordinate Plane (Ver 2)

- Author:
- Tim Brzezinski

- Topic:
- Coordinates, Geometry, Straight Lines, Reflection

## 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, the Mona Lisa is reflected about the xAxis. Drag points B, C, and the pre-image picture around and observe how her reflection changes.

## In the app above, move Lisa around to get different preimage points. Then, record their images in the image column.

Take a look at the table of data above. Notice any patterns? If so, describe!

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

**and**

*a*

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

**and**

*a*

*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.