## Symmetric translation

Given the point (4,3), determine the coordinates of the point obtained after a symmetric translation with respect to each of the following lines or points.

For example, y=2x. How would you do that? (I actually stumbled my professor at Kumon, which I was never able to do before with his instantaneous answers)

How about for the point (a,b)?

The solution says $a=\frac{x+4}{2}, b=\frac{y+3}{2}$

How do you get that?