# Exploring Rotations Around Points

- Author:
- Tim Brzezinski

- Topic:
- Rotation

## DIRECTIONS:

**point**,

*A***point**, and

*B***Daffy Duck's pic.**Select

**point**as the point about which to rotate the items you've just selected. For angle, enter . 2) Move the slider right and left. Note the

*C***images of points**(denoted as

*A*and*B**and*

**A'***). Feel free to move*

**B'****points**around as well. After doing so, please drag Daffy back in Quadrant 1. 3) Repeat step 1. This time, rotate Daffy Duck,

*A*and*B***point**, and

*A***point**

*about*

**B****point C**. 4) Repeat step 1. This time, rotate Daffy Duck,

**point**, and

*A***point**about

*B***point C**. After doing all this, please answer the questions that appear below the applet.

## 1.

**Let C = (0,0) be the point about which points A and B (and Daffy Duck) are rotated. **
Place

**point**and

*A*at (2, 3)**point**. When Daffy was rotated 90 degrees: What are the coordinates (

*B*at (5, 1)*x*,

*y*) of the image of

*What are the coordinates (*

**A**?*x*,

*y*) of the image of

*?*

**B**## 2.

**Let C = (0,0) be the point about which points A and B (and Daffy Duck) are rotated. **
Place

**point**and

*A*at (2, 3)**point**. When Daffy was rotated 180 degrees: What are the coordinates (

*B*at (5, 1)*x*,

*y*) of the image of

*What are the coordinates (*

**A**?*x*,

*y*) of the image of

*?*

**B**## 3.

**Let C = (0,0) be the point about which points A and B (and Daffy Duck) are rotated. **
Place

**point**and

*A*at (2, 3)**point**. When Daffy was rotated 270 degrees: What are the coordinates (

*B*at (5, 1)*x*,

*y*) of the image of

*What are the coordinates (*

**A**?*x*,

*y*) of the image of

*?*

**B**## 4.

**Let (0,0) be the point about which points A and B (and Daffy Duck) are rotated. **
Suppose the coordinates of

**point**Now even though we don't know what the coordinates of point

*A*are now labeled as (*x*,*y*).*A*are, can you write expressions (in terms of

*x*and/or

*y*) for the coordinates of the image of

*A*under a a) 90 degree counterclockwise rotation

**about (0,0)**? b) 180 degree counterclockwise rotation

**about (0,0)**? c) 270 degree counterclockwise rotation

**about (0,0)**?