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 the image of ΔABC after a clockwise rotation and translation, we first need to assess the similarity of the two triangles based on their corresponding side lengths and angles. The vertices of ΔABC are A(−4, 3), B(−3, 1), and C(−1, 2). Calculating the distances between the vertices yields side lengths that can be compared to those of ΔEFG, vertices E(4.5, 5), F(1.6, 3.8), and G(3, 1.5).

After calculating the side lengths for both triangles, it can be observed that the ratios of corresponding sides are not equal, indicating that the triangles are not similar. Therefore, although ΔABC can undergo transformations (rotation and translation), ΔEFG is not the image of ΔABC as they do not have the same shape or size.