Question

which sequence of transformations maps polygon abcd onto polygon wxyz?
a. a rotation of polygon abcd followed by a dilation of the image with a scale factor of 0.5
b. a reflection of polygon abcd followed by a dilation of the image with a scale factor of 0.5
c. a reflection of polygon abcd followed by a dilation of the image with a scale factor of 2
d. a rotation of polygon abcd followed by a dilation of the image with a scale factor of 2

Explanation:

Step1: Understand transformation properties

Rotation and reflection are rigid transformations (size - shape preserved). Dilation changes size.

Step2: Analyze scale factor

Since polygon \(WXYZ\) is larger than \(ABCD\), scale factor \(k> 1\).

Step3: Check transformation order

First, a reflection (to flip the orientation if needed, but here mainly the size change is key). Then a dilation with scale factor \(k = 2\) (by comparing side - lengths, e.g., if a side of \(ABCD\) is \(s\), a corresponding side of \(WXYZ\) is \(2s\)).

Answer:

C. a reflection of polygon \(ABCD\) followed by a dilation of the image with a scale factor of \(2\)