Like an engineer using a CAD program, understanding how a figure can be transformed allows you to manipulate it by sliding, flipping, turning, or resizing it. One way to practice this skill is to start with a figure, follow some instructions to transform it, and then draw the resulting figure. This can be done using plain paper, graphing paper, or a software program. Regardless of what technique you use, the important parts of the transformation need to be visualized mentally first.

Let's try a glide reflection which is a translation and a reflection. Take out a blank sheet of paper. Follow the instructions in the slideshow below.

Step 1 Fold the paper horizontally and then vertically. When you open it up, you should have a paper with four quadrants like the one shown below. Label the x and y axes along with quadrant numbers counterclockwise. Step 2 In the upper left quadrant (quadrant 2), draw a right triangle. Step 3 Flip the triangle over the y-axis. Think about what flipping the triangle does to the triangle. What direction does "over the y-axis" indicate? Is it a flip from left to right OR a flip from top to bottom? What should the result look like? Visualize this for your triangle and then draw it. Step 4 Slide the triangle down so that it ends up in the lower right quadrant. What type of transformation is a slide? How should the resulting triangle look? Where on the paper should it be? Conclusion Now you see how visualizing the transformation works. First, we formed a mental picture by asking questions at each step of the transformation; then we drew a picture. This visualization technique is often used by architects, designers, animators, and engineers to build very complex structures made from manipulating figures and shapes.