Reflection of a two dimensional figure in a line

Author:
Mathguru
We can see a triangle ABC in red color and a line ‘a’ in blue color. Equation of this line is y=mx+c and we can change the values of m and c using their respective slide bars. There is one more triangle A’B’C’ (green color). This triangle is the reflection of the triangle ABC in the line ‘a’.
Questions to think about: 1. Take any value of ‘m’ and ‘c’ and get a line ‘a’. On paper, calculate what are the ‘x’ and ‘y’ coordinates of the midpoints of AA’, BB’ and CC’. Now enter the calculated values of the ‘x’ coordinates in the equation of the line ‘a’ and get the corresponding values for the ‘y’ coordinates. What do we observe? 2. What is the relation between the co-ordinates of A and A’, B and B’ and C and C’ when m=0 (that is, the line ‘a’ is horizontal / parallel to the x-axis)? 3. What is the relation between the co-ordinates of A and A’, B and B’ and C and C’ when m=1 and c=0? 4. What is the relation between the co-ordinates of A and A’, B and B’ and C