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 ?

Answer 1

To determine if ΔEFG is similar to ΔABC and if it is the image of ΔABC, we need to analyze their shapes and sizes. First, we can calculate the side lengths of both triangles. The side lengths of ΔABC can be found using the distance formula, and similarly for ΔEFG.

However, without explicit calculations provided here, we can observe that the coordinates of ΔEFG are in a different quadrant compared to those of ΔABC, which suggests that after rotation and translation, the triangles have different positions in the coordinate plane. Additionally, the distances between the points in both triangles must be proportional for them to be similar. Given that the coordinates and configurations differ significantly, it is unlikely that ΔEFG is the image of ΔABC after rotation and translation, indicating that they are not similar either.