Which type of transformation does not preserve orientation?
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Solution
Perfect example of "oriented" figure on a plane is the right triangle ΔABC with sides AB=5,BC=3 and AC=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 directionA→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→Cis counterclockwise. That is a manifestation of (1) our triangle has orientation and (2) the transformation of reflection does not preserve the orientation.