Which type of transformation does not preserve orientation?

1 Answer
Zor Shekhtman
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 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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