Discover a translation through the composition of two reflections using Geogebra tools.

Using your prior knowledge of reflections, reflect triangle ABC over the line y=x+2. Compose another reflection of triangle A'B'C' over the line y=x-3.
What conclusions can you make about this composition of two reflections? How is triangle ABC related to triangle A"B"C"?Describe the translation that took place.
Construct a perpendicular line to line e and d. Construct a line segment between two lines on the perpendicular line in order to measure the distance between lines d and e.
Next, construct a line segment between any point on your pre image (point A, B, or C) and its corresponding point on your final image (point A", B", or C"). Measure this distance as well. What do you notice about the distance between these points compared to the distance between lines d and e?