Question

3 translate figure a 8 units to the left to form figure a’. then reflect figure a’ across the x - axis to form figure a’’. draw figures a’ and a’’. is figure a congruent to figure a’’? how do you know?

Explanation:

Step1: Understand translation rule

Translation 8 units to the left means subtracting 8 from the x - coordinates of all points of figure A to get figure A'.

Step2: Understand reflection rule

Reflection across the x - axis changes the sign of the y - coordinates of all points of figure A' to get figure A''.

Step3: Recall congruence property

Translations and reflections are rigid motions. Rigid motions preserve side - lengths and angle - measures.

Answer:

Yes, figure A is congruent to figure A'' because translations and reflections are rigid motions that preserve the size and shape of the figure.