Question

which series of transformations shows that hexagon a is congruent to hexagon b?
a. translate hexagon a 3 units down, rotate it 90° counterclockwise about the origin, and translate it 3 units to the right.
b. reflect hexagon a over the x - axis, reflect it over the y - axis, and translate it 3 units down.
c. rotate hexagon a 180° counterclockwise about the origin, reflect it over the y - axis, and translate it 3 units to the right.
d. reflect hexagon a over the x - axis, rotate it 90° counterclockwise about the origin, and translate it 3 units to the right.

Explanation:

Step1: Analyze Option A

• Translate down: changes vertical position.
• Rotate \(90^{\circ}\) counter - clockwise: changes orientation.
• Translate right: changes horizontal position. But the final orientation and position won't match.

Step2: Analyze Option B

• Reflect over \(x\) - axis: flips over \(x\) - axis.
• Reflect over \(y\) - axis: flips over \(y\) - axis.
• Translate down: moves down. This sequence will make the hexagon congruent.

Step3: Analyze Option C

• Rotate \(180^{\circ}\): changes orientation.
• Reflect over \(y\) - axis: flips.
• Translate right: moves. Won't match.

Step4: Analyze Option D

• Reflect over \(x\) - axis: flips.
• Rotate \(90^{\circ}\): changes orientation.
• Translate right: moves. Won't match.

Answer:

B. Reflect hexagon A over the x - axis, reflect it over the y - axis, and translate it 3 units down.