# Which type of transformation does not preserve orientation?

Dec 11, 2015

Reflection does not preserve orientation.
Dilation (scaling), rotation and translation (shift) do preserve it.

#### Explanation:

Perfect example of "oriented" figure on a plane is the right triangle $\Delta A B C$ with sides $A B = 5$, $B C = 3$ and $A C = 4$.

To introduce orientation, let's position ourselves above the plane and, looking down on this triangle, notice that the way from vertex $A$ to $B$ and then to $C$ can be viewed as the clockwise movement.

Rotation, translation (shift) or dilation (scaling) won't change the fact that the direction $A \to B \to C$ is clockwise.

Use now a reflection of this triangle relative to some axis. For instance, reflect it relative to a line $B C$. This transformation will leave vertices $B$ and $C$ in place (that is, $B ' = B$ and $C ' = C$), but vertex $A$ from being to the left of line $B C$ will move to the right of it to a new point $A '$.

The way $A ' \to B \to C$ is counterclockwise. That is a manifestation of (1) our triangle has orientation and (2) the transformation of reflection does not preserve the orientation.