Question

Gordon and Tess are trying to determine whether ΔABC and ΔFGE can be proven congruent through rigid motions. Gordon says that ΔABC ≅ ΔFGE because ΔABC can be reflected over the line x = 1 to create ΔFGE. Tess says ΔABC ≅ ΔFGE because ΔABC can be translated by the rule (x + 5, y − 7) to create ΔFGE. a coordinate grid with triangles ABC and EFG at A negative 7 comma 2, B negative 3 comma 6, C negative 2 comma 1, E 2 comma negative 1, F 7 comma negative 2, and G 3 comma negative 6 Who is correct?

A. Gordon only
B. Tess only
C. Both Gordon and Tess
D. Neither Gordon nor Tess

Answer 1

By analyzing the proposed rigid motions, we find that only Tess's suggestion of translating ΔABC by the rule (x + 5, y − 7) results in ΔFGE. Gordon's suggestion of reflecting over the line x = 1 does not create ΔFGE. Thus, the correct answer is B. Tess only.

Step-by-step explanation:

In order to determine whether ΔABC and ΔFGE can be proven congruent through rigid motions, we need to assess the validity of Gordon and Tess's claims. A rigid motion includes translations, rotations, and reflections that preserve the size and shape of geometric figures.

Gordon suggests that ΔABC can be reflected over the line x = 1 to create ΔFGE. Tess suggests that ΔABC can be translated by the rule (x + 5, y − 7) to create ΔFGE. Given the coordinates, we can apply each motion to ΔABC and see if it results in ΔFGE:

1. Reflection over x = 1: Reflecting a point (a, b) over the line x = 1 results in (2 - a, b). When we apply this to the points of ΔABC, we get points that do not match those of ΔFGE. Therefore, Gordon's claim is not correct.
2. Translation by (x + 5, y − 7): Translating each point of ΔABC by this rule results in a new set of points that match the coordinates of ΔFGE. Thus, Tess's claim is correct.

Since only Tess's claim holds true, the correct answer is B. Tess only.