Question

1. determine the transformations done on pentagon 1 to obtain pentagon 2.

a rotation followed by a reflection over the x-axis.
a dilation of 1/2 followed by a reflection over the x-axis.
a rotation followed by a dilation of 2.
a dilation of 2 followed by a reflection over the x-axis.

Explanation:

1. Size Comparison: Pentagon 2 is larger than Pentagon 1. A dilation factor greater than 1 (here, 2) enlarges a shape, while a factor less than 1 shrinks it. This rules out options with a dilation of $\frac{1}{2}$.
2. Position & Orientation: Pentagon 1 is in the first quadrant, and Pentagon 2 is in the second quadrant, flipped vertically. A reflection over the x-axis flips a shape across the x-axis, reversing its vertical orientation.
3. Order of Operations: First, dilate Pentagon 1 by a factor of 2 to match the size of Pentagon 2. Then, reflect the dilated shape over the x-axis to match the position and orientation of Pentagon 2. A rotation would not produce the exact mirrored vertical orientation seen here.

Answer:

A dilation of 2 followed by a reflection over the x-axis.