Question

which composition of similarity transformations maps △lmn to △lmn? a dilation with a scale factor less than 1 and then a reflection a dilation with a scale factor greater than 1 and then a reflection a dilation with a scale factor greater than 1 and then a translation

Explanation:

Step1: Analyze Dilation Scale Factor

First, compare the sizes of \( \triangle LMN \) and \( \triangle L'M'N' \). The image triangle \( \triangle L'M'N' \) is larger than the original \( \triangle LMN \), so the dilation scale factor must be greater than 1.

Step2: Analyze Transformation Type

Next, check the orientation and position. The original triangle is above the x - axis, and the image is below the x - axis, indicating a reflection (over the x - axis, for example). There's no translation (shift) as the relative position in terms of horizontal/vertical alignment (other than reflection) doesn't show a shift. So the transformation is a dilation with scale factor > 1 followed by a reflection.

Answer:

a dilation with a scale factor greater than 1 and then a reflection