Answer:
ΔABC is similar to ΔA'B'C'. because ΔA'B'C'. is obtained by dilating ΔABC by a scale factor of 1/4. and then rotating it about the origin by 180°.
Step-by-step explanation:
From the graph, we observe that the triangle was rotate 180°. That means the viable answers are the second and last option.
Now, we also notice that the dilation of the triangle is by a fraction, because it shrank. To find the right scale factor, we just have to compare coordinates.
The coordinates of ΔABC are A(4,-4); B(12,-4); C(8,-12).
The coordinates of ΔA'B'C' are A'(-1,1); B'(-3,1); C'(-2,3).
Notice that if we divide each corresponding coordinates, we have 4 as a scale factor, that is
A. [tex]\frac{4}{-1} =-4\\\frac{-4}{1}=-4[/tex]
B. [tex]\frac{12}{-3}=-4\\\frac{-4}{1}=-4[/tex]
C. [tex]\frac{8}{-2}=-4\\\frac{-12}{3}=-4[/tex]
As you can observe the decreasing scale factor is [tex]\frac{1}{4}[/tex], because if we divide the coordinates of ΔABC, we obtain the coordinates of ΔA'B'C'. It's important to consider the negative sign, it's part of the transformation.
Therefore, the right answer is the last choice.
ΔABC is similar to ΔA'B'C'. because ΔA'B'C'. is obtained by dilating ΔABC by a scale factor of 1/4. and then rotating it about the origin by 180°.
