Geometric Transformation (Reflecting a Triangle Over a Line)
In this geometric transformation triangle ABC is reflected over line MN. The initial triangle is green and its reflection is pink. You can move points M and N to change the position of the line of reflection (the red line). You can also move points A, B, or C to change the shape and the size of the green triangle.
1) What is the relationship between the coordinates of the vertices of the initial triangle and those of the reflected triangle?
2) Now, move points M and N on the x-axis. How does the relationship between the green triangle and the pink triangle changes? Analyze the relationship between the coordinates of vertices A, B, C and those of points A', B', and C'.
3) Move points M and N so that the equation of the reflection line is y=x. What is the relationship between points A, B, C and vertices A', B', C'?
This Geometric Transformation Activity was created by Doina Popovici with GeoGebra.