Question

Triangle A″B″C″ is formed by a reflection over x = −3 and dilation by a scale factor of 3 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C′? coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3 segment B double prime C double prime over segment BC equals one third segment AB over segment A double prime B double prime equals one third segment BC equals three segment A double prime B double prime segment A double prime B double prime equals three segment BC

Answer 1

Answer:

$\frac{AB}{A"B"} = \frac{1}{3}$

Step-by-step explanation:

Given

See attachment for $\triangle ABC$

Required

Determine the relationship between $\triangle ABC$ and $\triangle A"B"C"$

The reflection over $x =-3$ does not have any impact on the side lengths of both triangles because reflection does not alter side lengths and angles

The dilation from $\triangle ABC$ to $\triangle A"B"C"$ by scale factor 3 implies that:

$\frac{A"B"}{AB} = 3$

$\frac{B"C"}{BC} = 3$

$\frac{A"C"}{AC} = 3$

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

$\frac{AB}{A"B"} = \frac{1}{3}$

$\frac{BC}{B"C"} = \frac{1}{3}$

$\frac{AC}{A"C"} = \frac{1}{3}$

$\frac{AB}{A"B"} = \frac{1}{3}$ means that (b) is correct