Exploring Rotations Around Points
DIRECTIONS:
tool.
Highlight a box around point A, point B, and Daffy Duck's pic.
Select point C 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 images of points A and B (denoted as A' and B').
Feel free to move points A and B around as well. After doing so, please drag Daffy back in Quadrant 1.
3) Repeat step 1. This time, rotate Daffy Duck, point A, and point B about point C.
4) Repeat step 1. This time, rotate Daffy Duck, point A, and point B about 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 A at (2, 3) and point B at (5, 1). When Daffy was rotated 90 degrees: What are the coordinates (x, y) of the image of A? What are the coordinates (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 A at (2, 3) and point B at (5, 1). When Daffy was rotated 180 degrees: What are the coordinates (x, y) of the image of A? What are the coordinates (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 A at (2, 3) and point B at (5, 1). When Daffy was rotated 270 degrees: What are the coordinates (x, y) of the image of A? What are the coordinates (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 A are now labeled as (x, y). Now even though we don't know what the coordinates of point 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)?