Question

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 changes the x - coordinates of all points in figure A. If a point in figure A has coordinates (x,y), in figure A' its coordinates will be (x - 8,y).

Step2: Understand reflection rule

Reflection across the x - axis changes the sign of the y - coordinate. If a point in figure A' has coordinates (x',y'), in figure A'' its coordinates will be (x',-y').

Step3: Recall congruence property

Translations and reflections are rigid motions. Rigid motions preserve side - lengths and angle - measures. Since translations and reflections are rigid motions, figure A is congruent to figure A'' because rigid motions produce congruent figures.

Answer:

Yes, figure A is congruent to figure A'' because translations and reflections are rigid motions which preserve the shape and size (side - lengths and angle - measures) of the figure.