Question

pentagon abcde is similar to pentagon vwxyz. which sequence of transformations can be applied to abcde to produce vwxyz? a dilation with a scale factor of 2 followed by a rotation of 90° clockwise a rotation of 180° counterclockwise followed by a dilation with a scale factor of 2 a reflection over a vertical line followed by a dilation with a scale factor of \\( \frac { 1 } { 2 } \\) a translation to the right followed by a dilation with a scale factor of \\( \frac { 1 } { 2 } \\)

Explanation:

Step1: Analyze the scale factor

The length of \(AE = 36m\) and the length of \(VZ=18m\). The scale factor \(k=\frac{VZ}{AE}=\frac{18}{36}=\frac{1}{2}\).

Step2: Analyze the transformation

Since the two pentagons are similar, we need a dilation. Also, by observing the orientation (a reflection over a vertical line can make the orientation match). A reflection over a vertical line changes the orientation of the figure, and then a dilation with scale factor \(k = \frac{1}{2}\) changes the size.

Answer:

a reflection over a vertical line followed by a dilation with a scale factor of \(\frac{1}{2}\)