Reflection About a Point
Task
You are given triangle ABC with the corresponding vertices. Use the Input Box to enter the coordinates of a point P where you want to reflect triangle ABC. Enter the point in this format:
P = (x, y). Once you enter the point, GeoGebra will automatically reflect triangle ABC over point P and display the reflected triangle A′B′C′. Explore how the location of point P affects the reflected triangle!After reflecting triangle ABC over the point P you entered, what stays the same about the reflected triangle A′B′C′ compared to the original triangle ABC?
Reflect triangle ABC over point P = (3, 2). What are the coordinates of the reflected point A′? Explain how you found the answer. Generate a rule of finding the coordinates of the reflected objects given the point of reflection.
Try reflecting triangle ABC over three different points of your choice. How does changing the location of point P affect the position and orientation of the reflected triangle A′B′C′? Describe any patterns or rules you observe.