In the GeoGebra applet below:[br][br]1) Choose the ROTATE AROUND POINT [icon]/images/ggb/toolbar/mode_rotatebyangle.png[/icon] tool. [br] Highlight a box around[b][color=#1e84cc] point [i]A[/i][/color][/b], [b][color=#1e84cc]point [i]B[/i][/color][/b], and [b]Daffy Duck's pic.[/b][br] Select [b][color=#ff7700]point [i]C[/i][/color][/b] as the point about which to rotate the items you've just selected. [br] For angle, enter [math]90^\circ[/math]. [br][br]2) Move the slider right and left. Note the [b][color=#1e84cc]images of points [i]A[/i] and [i]B[/i][/color][/b] (denoted as [i][b][color=#1e84cc]A'[/color][/b][/i] and [i][b][color=#1e84cc]B'[/color][/b][/i]). [br] Feel free to move [b][color=#1e84cc]points [i]A[/i] and [i]B[/i][/color][/b] around as well. After doing so, please drag Daffy back in Quadrant 1.[br][br]3) Repeat step 1. This time, rotate Daffy Duck, [b][color=#1e84cc]point [i]A[/i][/color][/b], and [b][color=#1e84cc]point [/color][/b][i][b][color=#1e84cc]B[/color][/b] [math]180^\circ[/math][/i] about [b][color=#ff7700]point C[/color][/b].[br][br]4) Repeat step 1. This time, rotate Daffy Duck, [b][color=#1e84cc]point [i]A[/i][/color][/b], and [b][color=#1e84cc]point [i]B[/i][/color][/b] [math]270^\circ[/math] about [b][color=#ff7700]point C[/color][/b].[br][br]After doing all this, please answer the questions that appear below the applet.
[b][color=#ff7700]Let C = (0,0) be the point[/color] about which [color=#1e84cc]points [i]A[/i] and [i]B[/i] (and Daffy Duck)[/color] are rotated. [/b] [br]Place [b][color=#1e84cc]point [i]A[/i] at (2, 3)[/color][/b] and [b][color=#1e84cc]point [i]B[/i] at (5, 1)[/color][/b]. [br][br]When Daffy was rotated 90 degrees: [br] [br]What are the coordinates ([i]x[/i], [i]y[/i]) of the image of [i][b][color=#1e84cc]A[/color][/b]? [br][/i]What are the coordinates ([i]x[/i], [i]y[/i]) of the image of [i][b][color=#1e84cc]B[/color][/b][/i]?
[b][color=#ff7700]Let C = (0,0) be the point[/color] about which [color=#1e84cc]points [i]A[/i] and [i]B[/i] (and Daffy Duck)[/color] are rotated. [/b] [br]Place [b][color=#1e84cc]point [i]A[/i] at (2, 3)[/color][/b] and [b][color=#1e84cc]point [i]B[/i] at (5, 1)[/color][/b]. [br][br]When Daffy was rotated 180 degrees: [br][br]What are the coordinates ([i]x[/i], [i]y[/i]) of the image of [i][b][color=#1e84cc]A[/color][/b]? [br][/i]What are the coordinates ([i]x[/i], [i]y[/i]) of the image of [i][b][color=#1e84cc]B[/color][/b][/i]?
[b][color=#ff7700]Let C = (0,0) be the point[/color] about which [color=#1e84cc]points [i]A[/i] and [i]B[/i] (and Daffy Duck)[/color] are rotated. [/b] [br]Place [b][color=#1e84cc]point [i]A[/i] at (2, 3)[/color][/b] and [b][color=#1e84cc]point [i]B[/i] at (5, 1)[/color][/b]. [br][br]When Daffy was rotated 270 degrees: [br][br]What are the coordinates ([i]x[/i], [i]y[/i]) of the image of [i][b][color=#1e84cc]A[/color][/b]? [br][/i]What are the coordinates ([i]x[/i], [i]y[/i]) of the image of [i][b][color=#1e84cc]B[/color][/b][/i]?
[b][color=#ff7700]Let (0,0) be the point[/color] about which [color=#1e84cc]points [i]A[/i] and [i]B[/i] (and Daffy Duck)[/color] are rotated. [/b] [br]Suppose the coordinates of [b][color=#1e84cc]point [i]A[/i] are now labeled as ([i]x[/i], [i]y[/i]). [/color][/b][br][br]Now even though we don't know what the coordinates of point [i]A [/i]are, [br]can you write expressions (in terms of [i]x[/i] and/or [i]y[/i]) for the coordinates of the image of [i]A[/i] under a[br][br]a) 90 degree counterclockwise rotation [b][color=#ff7700]about (0,0)[/color][/b]? [br]b) 180 degree counterclockwise rotation [b][color=#ff7700]about (0,0)[/color][/b]?[br]c) 270 degree counterclockwise rotation [b][color=#ff7700]about (0,0)[/color][/b]?