# Transformations - 2. Rotation, Reflection, Dilation (aka Enlargement), and Translation

- Author:
- Angelique Errett, DavidA

In Task 1, you investigated TRANSLATIONS which is one type of transformation.
There are a total of four types of transformations we will explore this year in geometry.
They are:
1. TRANSLATIONS
2. ROTATIONS
3. REFLECTIONS
4. DILATIONS (called Enlargements in this exercise)
In this task, you will explore all these types to create your own definitions to describe how the different types of transformations move geometric figures through 2-dimensional space.
Use math vocabulary and complete sentences and be thorough and detailed.

## Activity 1.) Choose ROTATION as the type of transformation. Explore ROTATION by using the red slider below to change the ANGLE OF ROTATION.

Activity 2.) Using the same tool (called an applet) above, move the blue vertices of the triangle. Then use the red slider again to see the effects on the ROTATION.
Activity 3.) Lastly, move the CENTER OF ROTATION to overlie one of the blue vertices of the triangle. Use the red slider again to see how the triangle undergoes ROTATION in this situation.

## QUESTION #1. Develop a definition for ROTATION by describing the movement of the triangle relative to the CENTER OF ROTATION.

## QUESTION #2. What questions do you have about ROTATION? What do you wonder? What clarification do you need?

Activity 4.) Use the black slider above to choose REFLECTION as the type of transformation. Explore REFLECTION by moving the blue vertices of the triangle.
Activity 5.) This time move the LINE OF REFLECTION (the red dashed line) instead of the blue vertices of the triangle.

## QUESTION #3. Develop a definition for REFLECTION by describing the movement of the triangle relative to the LINE OF REFLECTION.

## QUESTION #4. What questions do you have about REFLECTION? What do you wonder? What clarification do you need?

Activity 6.) Use the black slider above to choose ENLARGEMENT (aka DILATION) as the type of transformation. Explore DILATION by moving the blue vertices of the triangle and the blue center of DILATION.
Activity 7.) Observe the way the image changes when compared with the original object when the scale factor (the red slider) is changed during DILATION.

## QUESTION #5. How does DILATION change the image of the original object? What role does the SCALE FACTOR play in changing the image?

## QUESTION #6. Use the movement of the image relative to the original object and the center and the scale factor to develop a definition for DILATION.

## QUESTION #7. What questions do you have about DILATION? What do you wonder? What clarification do you need?

Activity 8.) Use the black slider above to choose TRANSLATION as the type of transformation. Explore TRANSLATION by moving the blue vertices of the triangle.
Activity 9.) Use the red sliders to change the horizontal and vertical directions of the TRANSLATION vector.