Editing Cartesian coordinate system (section)

====Reflection====
If {{nowrap|(''x'', ''y'')}} are the Cartesian coordinates of a point, then {{nowrap|(−''x'', ''y'')}} are the coordinates of its [[coordinate rotations and reflections|reflection]] across the second coordinate axis (the y-axis), as if that line were a mirror. Likewise, {{nowrap|(''x'', −''y'')}} are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle <math>\theta</math> with the x-axis, is equivalent to replacing every point with coordinates {{nowrap|(''x'', ''y'')}} by the point with coordinates {{nowrap|(''x''′,''y''′)}}, where

<math display=block>
\begin{align}
x' &= x \cos 2\theta + y \sin 2\theta \\
y' &= x \sin 2\theta - y \cos 2\theta .
\end{align}
</math>

Thus:
<math display="block">(x',y') = ((x \cos 2\theta + y \sin 2\theta\,) , (x \sin 2\theta - y \cos 2\theta\,)) .</math>