Question

which composition of similarity transformations maps δlmn to δlmn? a dilation with a scale factor less than 1 and then a reflection a dilation with a scale factor less than 1 and then a translation 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, observe the size of the triangles. The image triangle \( \triangle L'M'N' \) is larger than the original \( \triangle LMN \), so the scale factor of dilation is greater than 1.

Step2: Analyze Transformation After Dilation

Next, check the position and orientation. After dilation (making it larger), a translation (shifting) is needed to map \( \triangle LMN \) to \( \triangle L'M'N' \). The other options with reflection don't match the orientation and position change here. So the composition is a dilation with scale factor >1 and then a translation.

Answer:

a dilation with a scale factor greater than 1 and then a translation (the option corresponding to this description in the choices, likely the last or relevant one with dilation >1 and translation)