Question

alec said that the figures are similar because figure a is the result of dilating figure a about the origin with a scale factor of 1/2 and then reflecting it over the y - axis. which corrects alecs error? a. the image was instead a dilation about the origin with a scale factor of 2. b. instead of being reflected after being dilated, the image was translated 4 units to the left and 2 units up. c. the image was instead a dilation about the origin with a scale factor of 2, and then it was translated 4 units to the left and 2 units up. d. instead of being reflected over the y - axis, the image was reflected over the line y = x.

Explanation:

Step1: Analyze dilation

A dilation about the origin with a scale - factor of $\frac{1}{2}$ would make the coordinates of each point of Figure A half of the original coordinates. But if the scale - factor was 2 as in the wrong statement, the image would be larger.

Step2: Analyze reflection

Reflecting over the y - axis changes the sign of the x - coordinate of each point.

Step3: Analyze translation

Translation moves the figure without changing its shape or orientation. In the wrong statement, the translation details are incorrect. The correct sequence is dilation with scale factor $\frac{1}{2}$, reflection over the y - axis, and then translation.
The correct sequence of transformations from Figure A to Figure A' is: dilation about the origin with a scale factor of $\frac{1}{2}$, reflection over the y - axis, and then translation 4 units to the left and 2 units up.

Answer:

The image was dilated about the origin with a scale factor of $\frac{1}{2}$, then reflected over the y - axis, and then translated 4 units to the left and 2 units up.