**EMAT
6700**

**by
Brad Simmons**

**Transformations and Reflections**

Use geometer's sketchpad investigate transformations and reflections.

Transformations

The figure above shows how triangle ABC is mapped to triangle XYZ.

Each point of triangle ABC with coordinates ( x, y ) is mapped to triangle XYZ with coordinates ( x+6, y-3).

Please click here for a geometer's sketchpad sketch of the figure shown above.

**Use geometer's sketchpad to draw the transformation image
described below.**

1. Map triangle ABC (shown above) with coordinates ( x, y ) to triangle XYZ with coordinates ( x-4, y ).

2. Map triangle ABC (shown above) with coordinates ( x, y ) to triangle XYZ with coordinates ( x+8, y+7 ).

3. Map triangle ABC (shown above) with coordinates ( x, y ) to triangle XYZ with coordinates ( -x, -y ).

Reflections

The figure shown above shows how triangle ABC is mapped onto triangle XYZ. The transformation is each point of triangle ABC with coordinates ( x, y ) is mapped to triangle XYZ with coordinates ( -x+6, y ). The triangle XYZ is the reflected image of triangle ABC with respect to the red vertical line with an equation of x = 3.

Please click here for a geometer's sketchpad sketch of the figure shown above.

**Use geometer's sketchpad to draw the reflected image
described below. The reflection is with respect to what line?**

1. Map triangle ABC (shown above) with coordinates ( x, y ) to triangle XYZ with coordinates ( -x-4, y ).

2. Map triangle ABC (shown above) with coordinates ( x, y ) to triangle XYZ with coordinates ( x, -y+8 ).