Question

mathematics progress check
which series of transformations shows that pentagon a is congruent to pentagon b?
pentagon a
pentagon b
a. rotate pentagon a 90° clockwise about the origin, reflect it over the x - axis, and translate it 6 units to the left.
b. reflect pentagon a over the y - axis, rotate it 180° clockwise about the origin, and translate it 3 units up.
c. rotate pentagon a 90° clockwise about the point (1, 1), reflect it over the x - axis, and translate it 3 units to the left.
d. reflect pentagon a over the y - axis and translate it 2 units to the left and 8 units up.

Explanation:

Step1: Analyze Option A

• Rotate pentagon A \(90^{\circ}\) clockwise about the origin: Changes the orientation.
• Reflect over the \(x -\)axis: Flips it vertically.
• Translate 6 units to the left: Moves it horizontally. This sequence of transformations aligns pentagon A with pentagon B.

Step2: Analyze Option B

• Reflect over the \(y -\)axis: Flips horizontally.
• Rotate \(180^{\circ}\) clockwise: Changes orientation.
• Translate 3 units up: Moves vertically. This does not align with pentagon B.

Step3: Analyze Option C

• Rotate about \((1,1)\): Non - standard center.
• Reflect over \(x -\)axis: Flips vertically.
• Translate 3 units left: Moves horizontally. Misaligns.

Step4: Analyze Option D

• Reflect over \(y -\)axis: Flips horizontally.
• Translate 2 left and 8 up: Moves. Misaligns.

Answer:

A. Rotate pentagon A \(90^{\circ}\) clockwise about the origin, reflect it over the \(x -\)axis, and translate it 6 units to the left.