Use the construction to explore rotations. Use the slider to change the angle of rotation and the check boxes to toggle various parts of the construction. Also, feel free to move the position of the Preimage or its vertices, and/or the center of the rotation. Use the questions below to guide your exploration.

[list][br][*]What do you notice? I noticed that when you move the slider up or down, it can increase or decrease the rotation of an image.[/*][/list][br][list][br][*]What do you wonder? I wonder how having different center of rotations impacts an image’s translation [/*][/list][list][br][*]Compare the properties of the image and pre-image (i.e., side lengths, angles, etc.). What do you notice? When the image rotates around the center point/ origin, it goes through an isometric translation keeping the same angle measurements and lengths as the ones from the pre-image; but their coordinates change instead.[/*][/list] [b]Part C:[/b][br][list][br][*]What patterns did you notice? I noticed that the coordinates of each figure (pre-image and image), would have their x and y values swapped with each other; and either be positive of negative depending on which ever quadrant they are located on.[/*][*] Based on this pattern, can you determine a rule for finding the coordinates of a figure after completing a 90-degree counterclockwise rotation?            Based on this pattern, it is possible to find the coordinates of a figure that has completed a 90-degree counter clockwise rotation.[/*][*]What do you predict might be the rule for rotating an image 180-degrees counterclockwise about the origin?  The rule for rotating an image 180-degrees, would be to use the same coordinates from the pre-image; and make them positive or negative, depending on which quadrant the 180 degree rotation is located on.[/*][/list]                     [b]Part D:[/b][list][*]What patterns did you notice? With 180 degree rotations, I noticed the the coordinates of the vertex are almost identical, except for the fact that they are positive/negative depending on the quadrant.[br][/*][*] Based on this pattern, can you determine a rule for finding the coordinates of a figure after completing a 180-degree counterclockwise rotation?         Based on this pattern, it is possible to determine the coordinates of a figure after an 180-degree counterclockwise rotation.[br][/*][/list]