Question

determining the similarity transformation
which composition of similarity transformations would map polygon abdc to polygon abdc?
○ a dilation with a scale factor greater than 1 and then a translation
○ a dilation with a scale factor greater than 1 and then a rotation
× 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

Explanation:

Step1: Analyze Dilation Scale Factor

Compare the size of polygon ABDC and A'B'D'C'. Polygon A'B'D'C' is larger, so the scale factor of dilation (to map ABDC to A'B'D'C') must be greater than 1 (since dilation with scale factor >1 enlarges the figure).

Step2: Analyze Transformation Type After Dilation

Check the orientation and position. After dilation (enlarging ABDC), a translation (shifting) would align the figures, as the shapes have the same orientation (no rotation or reflection needed). Rotation would change orientation, reflection flips, but here the direction is same, just position shifted. The incorrect marked option used scale factor <1 (which shrinks, but we need to enlarge), so the correct composition is dilation (scale >1) then translation.

Answer:

a dilation with a scale factor greater than 1 and then a translation