**Theorem 4.6**: The
reflection of the
point *A *in a line is

where* **F *is the foot of
the point* A *in the line.

**Proof**: By the definition of a
reflection, to get from a
point * A *to its reflection, move along the
line determined by* **A *and* **F** *and go a distance on
the other
side of* F *from* **A, *which is the same as the distance from* A *to* **F*.* *Then by Theorem 2.1,
the reflection of* **A*,* **R*(*A*),* *will be a point of the form* ** ** *

where, by Theorem 2.2

Since the distance
from* **A *to* **F *is the same as the distance from* **F *to* **R*(*A*),* **t* = 2,* *and the result follows.