Answer these two questions in 3-5 sentences. Are the figures similar? Triangle ABC has vertices A(-4, 3)B(-3, 1)C(-1, 2). Triangle ABC is rotated clockwise about the origin and then translated. Triangle EFG has vertices E(4.5, 5)F(1.6), 3.8)G(3, 1.5). Is triangle EFG the image of ABC

Answer 1

To determine if triangles ABC and EFG are similar, we first need to analyze their vertices and the transformations applied. Triangle ABC has vertices A(-4, 3), B(-3, 1), and C(-1, 2), and after a clockwise rotation and a translation, we need to see if the resultant triangle can match the specifications of triangle EFG, which has vertices E(4.5, 5), F(1.6, 3.8), and G(3, 1.5).

Calculating the side lengths of both triangles and checking for proportionality is necessary to conclude similarity. If the transformation from ABC to EFG maintains the shape—meaning the angles remain the same and the sides are in proportion—then the triangles can be considered similar. Additionally, once the rotations and translations are applied, if the new vertices align correctly, EFG could indeed be the image of triangle ABC.