Investigating Reflections

Author:
tmarley

Part A

1. Use the "Reflect about Line" tool to reflect ABCD over line EF to produce A'B'C'D'. 2. Drag the points of the line of reflection and on ABCD to observe how the preimage, image, and line of reflection are related. What happens when the line of reflection passes through the shape? 3. Make four segments that connect A to A', B to B', etc. How do these segments relate to the line of reflection? What geometric properties do you notice?

Part B

1. Use the "Reflect about Line" tool to reflect triangle ABC about the y-axis. How are the coordinates of the image and the preimage related? 2. Use the "Reflect about Line" tool to reflect triangle ABC about the x-axis. How are the coordinates of the image and the preimage related? 3. What conclusions can you make about what happens to the coordinates when reflecting over the y-axis? The x-axis?

Part C

1. Graph the line y = x on the graph below. (Choose two points on the line y = x and then connect them with the line tool.) 2. Then use the point tool to decide where the points A', B', and C' should be located if triangle ABC is reflected about the line y = x. Connect the points with segments to make a new triangle. 3. What happens to the coordinates when a shape is reflected about the line y = x? What generalizations can you make?

Part D

1. Thinking about the geometric properties you noticed in the investigations above, see if you can reflect triangle CDE about line AB using only the tools provided. 2. After you have completed the reflection, drag the points C, D, E, A, and B around to verify that your reflection always works regardless of the location and size of the preimage triangle.

Part E

1. Graph the line y = -x on the graph below. (Choose two points on the line y = -x and then connect them with the line tool.) 2. Then use the point tool to decide where the points A', B', and C' should be located if triangle ABC is reflected about the line y = -x. Connect the points with segments to make a new triangle. 3. What happens to the coordinates when a shape is reflected about the line y = -x? What generalizations can you make?