Use the image to answer the question. Answer these two questions in 3–5 sentences. Are the figures similar? ΔABC has vertices A(−4,3) , B(−3,1) , and C(−1,2) . ΔABC is rotated clockwise about the origin and then translated. ΔEFG has vertices E(4.5,5) , F(1.6,3.8) , and G(3,1.5) . Is ΔEFG the image of ΔABC ? (4 points)

Answer 1

To determine whether triangles ΔABC and ΔEFG are similar, we can analyze the coordinates of their vertices. The figures will be similar if they have the same shape, which means that the angles must be congruent and the sides must be proportional.

Next, let's examine the transformations. If ΔABC is rotated clockwise and then translated, it can potentially match the size and angles with ΔEFG. However, based on the coordinates of the vertices, we can see that the lengths of sides and angles do not appear to remain proportional post-transformation. Specifically, if we calculate the side lengths of both triangles using the distance formula, it may reveal a lack of proportionality, indicating that ΔEFG is not the image of ΔABC. Thus, ΔABC and ΔEFG are not similar figures.