Question

which transformations could be performed to show that △abc is similar to △a\b\c\? a reflection over the x-axis, then a dilation by a scale factor of 3 a reflection over the x-axis, then a dilation by a scale factor of 1/3 a 180° rotation about the origin, then a dilation by a scale factor of 3 a 180° rotation about the origin, then a dilation by a scale factor of 1/3

Explanation:

Step1: Identify coordinates of △ABC

From the graph: A(-8,4), B(-8,8), C(0,4)

Step2: Identify coordinates of △A'B'C'

From the graph: A'(2,-1), B'(2,-2), C'(0,-1)

Step3: Check reflection over x-axis

Reflection over x-axis: (x,y)→(x,-y). A(-8,4)→(-8,-4), B(-8,8)→(-8,-8), C(0,4)→(0,-4)

Step4: Calculate scale factor

Compare reflected points to △A'B'C': $\frac{2}{-8}=-\frac{1}{3}$ (absolute value $\frac{1}{3}$), $\frac{-1}{-4}=\frac{1}{3}$. Scale factor is $\frac{1}{3}$

Answer:

B. a reflection over the x-axis, then a dilation by a scale factor of $\frac{1}{3}$