Answer:
[tex]\frac{AB}{A"B"} = \frac{1}{3}[/tex]
Step-by-step explanation:
Given
See attachment for [tex]\triangle ABC[/tex]
Required
Determine the relationship between [tex]\triangle ABC[/tex] and [tex]\triangle A"B"C"[/tex]
The reflection over [tex]x =-3[/tex] does not have any impact on the side lengths of both triangles because reflection does not alter side lengths and angles
The dilation from [tex]\triangle ABC[/tex] to [tex]\triangle A"B"C"[/tex] by scale factor 3 implies that:
[tex]\frac{A"B"}{AB} = 3[/tex]
[tex]\frac{B"C"}{BC} = 3[/tex]
[tex]\frac{A"C"}{AC} = 3[/tex]
The above equations mean that options (c) and (d) are incorrect because A"B" does not correspond to BC
Take inverse of the above equations
[tex]\frac{AB}{A"B"} = \frac{1}{3}[/tex]
[tex]\frac{BC}{B"C"} = \frac{1}{3}[/tex]
[tex]\frac{AC}{A"C"} = \frac{1}{3}[/tex]
[tex]\frac{AB}{A"B"} = \frac{1}{3}[/tex] means that (b) is correct
