Question

AEFI is dilated by a scale factor of 1/3 with the center of dilation at point F. Then, it is reflected over line a to create AHFG. Based on these transformations, which statement is true?

A. AHFG is congruent to AEFI.
B. AEFI is congruent to HFGA.
C. AEFI is similar to AHFG.
D. AHFG is a translation of AEFI.

Answer 1

AEFI, after being dilated by 1/3 and reflected over line a to create AHFG, remains similar to AHFG. This is due to the properties of dilation and reflection in geometry.

Step-by-step explanation:

Given that figure AEFI is dilated by a scale factor of 1/3 with the center of dilation at point F, and then reflected over line a to create AHFG, the resulting figure AHFG is neither congruent nor identical in size to AEFI. Instead, AHFG is a reduced copy of AEFI. Therefore, the correct answer to the student's question is 'AEFI is similar to AHFG', which aligns with option C. After a dilation, the shapes are still similar because they have the same shape but are different in size. A reflection does not change the size or shape, therefore the similarity is maintained.