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A similarity transformation consisting of a reflection
and a dilation is performed on a figure, and one point maps to itself. Explain how this can happen.

Sagot :

If the point in question is on the line of reflection, then the point won't move. Any point on a line of reflection stays where it is.

If that same point is the center of dilation, then it also doesn't move. The center of dilation is the only point that doesn't move in a dilation.

So the two conditions are:

  • The point must be on the line of reflection
  • The point must be the center of dilation

These two facts mean that the line of reflection must go through the center of dilation.

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