# Rotations in the Coordinate Plane

- Author:
- Brooke Becker

- Topic:
- Rotation

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.
a) Move the slider (the angle of rotation about the origin) to 90 degrees, 180 degrees, 270 degrees, and 360 degrees.
b) What do you notice about the coordinates of the image (red) in comparison to the coordinates of the pre-image (blue)?
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.
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:
a) A'B'C'D' is a 90 degree counterclockwise rotation about the origin
b) A'B'C'D' is a 180 degree counterclockwise rotation about the origin
c) A'B'C'D' is a 270 degree counterclockwise rotation about the origin
2) Graph the quadrilateral to check your answer