Question

abcd is a square. given abcd≅abcd, describe a pair of rigid motions that maps abcd to abcd
choose the correct answer below.
a. translation 6 units down, translation 6 units right
b. reflection across the x - axis, translation 7 units right
c. reflection across the x - axis, translation 6 units up
d. translation 6 units up, translation 6 units left

Explanation:

Step1: Analyze translation in option A

Translation 6 units down moves the square down - ward and then 6 units right moves it to the right. But this does not map the given square to the target square.

Step2: Analyze option B

Reflection across the x - axis flips the square over the x - axis and then translation 7 units right moves it horizontally. This does not map the square correctly.

Step3: Analyze option C

Reflection across the x - axis flips the square over the x - axis and translation 6 units up moves it vertically. This does not map the square as required.

Step4: Analyze option D

Translation 6 units up moves the square vertically upward and then 6 units left moves it horizontally to the left. By observing the position of the square ABCD and A'B'C'D' on the grid, this pair of translations maps ABCD to A'B'C'D'.

Answer:

D. Translation 6 units up, translation 6 units left