Question

10 esmeralda which description of a figure and its image match the transformation described by (x,y)→(x,3y)? a the figure and its image are similar and the image has been translated 3 units up. b the figure and its image are similar and the image has been translated 3 units to the right. c the figure and its image are similar and the image has been stretched horizontally. d the figure and its image are neither similar nor congruent, and the image has been stretched vertically. e the figure and its image are neither similar nor congruent, and the image has been stretched vertically.

Explanation:

Step1: Analyze the transformation

The transformation $(x,y)\to(x,3y)$ multiplies the $y -$coordinate of each point by 3. This is a vertical stretch. Since the ratio of corresponding side - lengths of the original figure and the image is a non - one constant (3 in this case), the figure and its image are similar.

Step2: Evaluate each option

Option A is incorrect because it mentions a translation 3 units up which is not the case here. Option B is incorrect as it mentions a translation 3 units to the right. Option C is incorrect because the figure and its image are similar. The correct transformation is a vertical stretch and the figure and its image are similar.

Answer:

The figure and its image are similar and the image has been stretched vertically.