Question

which composition of similarity transformations maps polygon abcd to polygon abcd? a dilation with a scale factor less than 1 and then a reflection a dilation with a scale factor less than 1 and then a translation a dilation with a scale factor greater than 1 and then a reflection a dilation with a scale factor greater than 1 and then a translation

Explanation:

• Dilation Scale Factor:
• Observe the size of polygon \(A'B'C'D'\) compared to \(ABCD\). Since \(A'B'C'D'\) is smaller than \(ABCD\), the scale factor of the dilation is less than \(1\). A dilation with a scale factor \(k<1\) reduces the size of the figure.
• Transformation Type (Reflection vs Translation):
• A reflection flips a figure over a line. A translation slides a figure without flipping it. Looking at the orientation of the polygons, if we consider the coordinate - plane, the orientation of \(A'B'C'D'\) is such that it is a mirror - image (reflection) of \(ABCD\) (after size reduction). If it were a translation (after dilation), the orientation (the way the vertices are ordered in terms of left - right/up - down) would remain the same.

Answer:

a dilation with a scale factor less than 1 and then a reflection