Education Technology

Middle Grades Math: Reflections and Rotations

by Texas Instruments


  • 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

About the Lesson

  • 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.