Use the image to answer the question.

Question

Triangle A B C is drawn with a solid line and is located in quadrant 2 of a coordinate plane. Triangle E F G is drawn with a dotted line and is located in quadrant 1. Angle A and Angle E are labeled as equivalent angles measuring 45 degrees.

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

The figures ΔABC and ΔEFG are similar because they have corresponding angles that are equal; specifically, angle A in ΔABC and angle E in ΔEFG both measure 45 degrees. Additionally, if ΔABC can be transformed into ΔEFG through a combination of rotation and translation, this further supports their similarity.

To determine if ΔEFG is the image of ΔABC, we must consider both transformations. The vertices of ΔABC would need to be rotated and translated appropriately to match the coordinates of ΔEFG. Since the coordinates do not match up directly after considering possible rotations and translations, ΔEFG is not the direct image of ΔABC, but they remain similar figures due to their corresponding angles.