Use the following construction to look at counterclockwise rotations of a triangle in the coordinate plane. The pre-image or the original image is blue, and the image or the image after the translation (in this case, rotation about the origin) is red.[br]a) Move the slider (the angle of rotation about the origin) to 90 degrees, 180 degrees, 270 degrees, and 360 degrees.[br]b) What do you notice about the coordinates of the image (red) in comparison to the coordinates of the pre-image (blue)?[br]c) Make a conjecture about each of the coordinates after a 90 degree, 180 degree, and 270 degree counterclockwise rotation about the origin.

Based on your conjecture, answer the following without graphing the quadrilateral ABCD.[br]1) If the pre-image is a quadrilateral with coordinates A(2,2), B(5,2), C(5, 7), and D(1,6), what are the coordinates of each of the following images:[br]a) A'B'C'D' is a 90 degree counterclockwise rotation about the origin[br]b) A'B'C'D' is a 180 degree counterclockwise rotation about the origin[br]c) A'B'C'D' is a 270 degree counterclockwise rotation about the origin[br]2) Graph the quadrilateral to check your answer