Students will reflect figures over the x- and y-axes. By studying what happens to the coordinates of the pre-image and image points, they will write rules for reflecting points over the axes. Students will then rotate figures about the origin, in both clockwise and counterclockwise directions. Again, they will study what happens to the coordinates of the pre-image and image points to write rules for reflecting points 90° and 180° about the origin.

• Rotate and reflect two-dimensional figures in a coordinate plane.
• Analyze the coordinates of numerous rotated and reflected figures to determine the rules of geometric transformations.
• Use abstract and quantitative reasoning to explore relationships among pre-image and image figures.

• reflection
• rotation
• transformation

• Students will reflect figures over the x- and y-axes. By studying what happens to the coordinates of the pre-image and image points, they will write rules for reflecting points over the axes.
• Students will then rotate figures 90°, 180°, and 270° counterclockwise about the origin, studying the coordinates of the pre-image and the image to write rules for rotations. In Problem 3, students can use the “grab and move” feature to explore other reflections and rotations.