Question

determining the similarity transformation
which composition of similarity transformations would map polygon abdc to polygon abdc?
options:

• 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 translation
• a dilation with a scale factor less than 1 and then a reflection
• a dilation with a scale factor greater than 1 and then a rotation

image of coordinate grid with polygons abdc and abdc

Explanation:

Step1: Analyze Dilation Scale Factor

Compare the size of polygon \(ABDC\) and \(A'B'D'C'\). The image \(A'B'D'C'\) is larger than the pre - image \(ABDC\), so the scale factor of dilation must be greater than 1.

Step2: Analyze Transformation Type After Dilation

Looking at the orientation and position, after dilation (making it larger), a translation (shifting) is used to map \(ABDC\) to \(A'B'D'C'\). There is no reflection (since the orientation is the same) or rotation (the general direction of the sides is preserved in a translational way after dilation) involved. So the composition is a dilation with a scale factor greater than 1 and then a translation.

Answer:

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