# Rotations/Dilations

For each diagram, describe a translation, rotation, or reflection that takes line ℓℓ to line ℓ′ℓ′. Then plot and label A′A′ and B′B′, the images of AA and BB.
1. 2. New Question Use a piece of tracing paper to trace lines aa and bb and point KK. Then use that tracing paper to draw the images of the lines under the three different transformations listed.As you perform each transformation, think about the question:What is the image of two parallel lines under a rigid transformation?
1. Translate lines aa and bb 3 units up and 2 units to the right.
• What do you notice about the changes that occur to lines aa and bb after the translation?
• What is the same in the original and the image?
2. Rotate lines aa and bb counterclockwise 180 degrees using KK as the center of rotation.
• What do you notice about the changes that occur to lines aa and bb after the rotation
• What is the same in the original and the image?
3. Reflect lines aa and bb across line hh.
• What do you notice about the changes that occur to lines aa and bb after the reflection?
• What is the same in the original and the image?
Here is a triangle. 1. Reflect triangle ABCABC over line ABAB. Label the image of CC as C′C′.
2. Rotate triangle ABC′ABC′ around AA so that C′C′ matches up with BB.
3. What can you say about the measures of angles BB and CC?
In the activity, we made a parallelogram by taking a triangle and its image under a 180-degree rotation around the midpoint of a side. This picture helps you justify a well-known formula for the area of a triangle. What is the formula and how does the figure help justify it?