Question

in the figure shown, which composition of rigid transformations will map one triangle onto the other?
a. a glide reflection
b. a reflection followed by a translation
c. two translations
d. a rotation followed by a translation

Explanation:

1. Analyze each option:

• A glide - reflection is a translation followed by a reflection in a line parallel to the translation vector.
• A reflection followed by a translation: A reflection flips the triangle over a line, and then a translation moves it to the new position.
• Two translations just move the triangle without changing its orientation in a non - rotational or reflective way.
• A rotation followed by a translation: First, the triangle is rotated around a point, and then it is moved to the final position.
• By observing the orientation of the two triangles, we can see that one triangle needs to be rotated to match the orientation of the other and then translated to match the position.

Answer:

D. a rotation followed by a translation