Question

which description of a figure and its image match the transformation described by (x,y)→(2x,2y + 1)? a the figure and its image are similar, but not congruent, and the image has been translated 1 unit up. b the figure and its image are similar, but not congruent, and the image has been translated 1 unit to the right. c the figure and its image are congruent and the image has been translated 1 unit up. d the figure and its image are congruent and the image has been translated 1 unit to the right.

Explanation:

Step1: Analyze the transformation rule

The transformation $(x,y)\to(2x,2y + 1)$ has two - part changes. The $x$ - coordinate is multiplied by 2 and the $y$ - coordinate is multiplied by 2 and then 1 is added.

Step2: Determine similarity and congruence

Since the coordinates are multiplied by 2 (a non - 1 scale factor), the figure and its image are similar but not congruent.

Step3: Analyze the vertical translation

The addition of 1 to the $2y$ term in the $y$ - coordinate transformation means the image is translated 1 unit up.

Answer:

A. The figure and its image are similar, but not congruent, and the image has been translated 1 unit up.