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 if figures ΔABC and ΔEFG are similar, we can compare the corresponding side lengths and angles of both triangles after transformations. First, we calculate the lengths of the sides of ΔABC using the distance formula. Once we find the lengths, we can analyze if they maintain the same ratio as the corresponding sides of ΔEFG.

After performing the necessary transformations on ΔABC, such as the rotation and translation, if the corresponding angles remain equal and the lengths of the sides maintain a constant ratio, then ΔEFG can indeed be considered the image of ΔABC. However, without calculating the specific lengths and angles, we cannot definitively conclude their similarity just based on the vertex coordinates.