Question

Triangle ABC underwent a sequence of transformations to give triangle A′B′C′. Which transformations could not have taken place?

A.
a reflection across the line y = x followed by a reflection across the line y = -x

B.
a reflection across the x-axis followed by a reflection across the y-axis

C.
a rotation 180° clockwise about the origin followed by a reflection across the line y = x

D.
a reflection across the y-axis followed by a reflection across the x-axis

Answer 1

Answer:  The answer is (C) a rotation 180° clockwise about the origin followed by a reflection across the line y = x.

Step-by-step explanation:  Triangle A'B'C' is formed after a number of sequences applied to the triangle ABC.

We are to select the correct transformations that could not take place.

Option (A) is "a reflection across the line y = x followed by a reflection across the line y = -x".

These transformations will map ΔABC to ΔA'B'C', so this option is incorrect.

Option (B) is "a reflection across the x-axis followed by a reflection across the y-axis".

These transformations will map ΔABC to ΔA'B'C', so this option is incorrect.

Option (C) is "a rotation 180° clockwise about the origin followed by a reflection across the line y = x".

These transformations will not map ΔABC to ΔA'B'C', so this option is correct.

Option (D) is "a reflection across the y-axis followed by a reflection across the x-axis".

These transformations will map ΔABC to ΔA'B'C', so this option is incorrect.

Thus, (C) is the correct option.

Answer 2

Answer: C is the answer.

Step-by-step explanation: A'B'C' is rotating forward which is clockwise because counterclockwise goes backwards.