Which type of transformation does not preserve orientation?

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Which type of transformation does not preserve orientation?

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Answer 1 · 2015-12-11T03:48:07

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 $Delta ABC$ with sides $AB=5$ , $BC=3$ and $AC=4$ .
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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 $A->B->C$ is clockwise.

Use now a reflection of this triangle relative to some axis. For instance, reflect it relative to a line $BC$ . 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 $BC$ will move to the right of it to a new point $A'$ .

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

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Which type of transformation does not preserve orientation?

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