**Theorem 4.7**: The
reflection of the
poin*t** *(*x*_{1},
*y*_{1})* *in the line
* y* = *mx* + *b *is

The reflection of the
point * *(*x*_{1},
*y*_{1})* *in the vertical
line * **x* = *a *is

**Proof**: Let* **A* = (*x*_{1}, *y*_{1}),* *and let* **F *be
the foot of the
point * **A* in the line. By
Theorem 4.6,

If the line is the
vertical
line * x* = *a*,* *then

and, for the case of the vertical line, the result follows.

If the line is not vertical it will have an equation of the form

by Theorem 1.2, and by Theorem 1.10

So