Equations defining Plane Reflection/Examples

Examples of Equations defining Plane Reflections

$x$-Axis

Let $\phi_x$ denote the reflection in the plane whose axis is the $x$-axis.

Let $P = \tuple {x, y}$ be an arbitrary point in the plane

Then:

$\map {\phi_x} P = \tuple {x, -y}$

$y$-Axis

Let $\phi_y$ denote the reflection in the plane whose axis is the $y$-axis.

Let $P = \tuple {x, y}$ be an arbitrary point in the plane

Then:

$\map {\phi_y} P = \tuple {-x, y}$