Question

Find the image of the letter for a reflection first across line L and then across line M. Is the resulting transformation a translation or a​ rotation? For a​ translation, describe the direction and distance. For a​ rotation, tell the center of rotation and the angle of rotation. (look at the screenshot)

Which of the following shows the image in​ blue?
A. (look at pic)
B. (look at pic)
C. (look at pic)
Which of the following describes the resulting​ transformation?
A. It is a rotation about the point C. The angle of rotation is 76° clockwise.
B. It is a translation down and to the right. The distance of the translation is twice the distance between the letter and M.
C. It is a translation down and to the right. The distance of the translation is the distance between the letter and M.
D. It is a rotation about the point C. The angle of rotation is 152° clockwise.

Answer 1

A. Image in blue: C

B. Resulting transformation: D

Step-by-step explanation:

In part A, option C is the correct choice as it accurately represents the image in blue after undergoing reflections across lines L and M. Reflections involve flipping an object over a line, and the visual match between the transformed image and option C confirms its correctness. For part B, option D is the accurate selection. The resulting transformation is a rotation, evidenced by the change in orientation of the letter. The description of a rotation about point C with a 152° clockwise angle corresponds with the observed changes in the letter's position.

Understanding geometric transformations, such as reflections and rotations, is essential for solving problems in geometry. Recognizing the effects of these transformations allows for accurate interpretation of visual representations. In this case, identifying the correct options involves a keen awareness of how letters or shapes change when subjected to specific transformations.

Practicing similar problems enhances one's ability to decipher and apply geometric concepts. Accurate choices in this context reflect a solid grasp of spatial relationships and geometric principles, contributing to a broader mathematical proficiency.