Question

select all the correct answers
which sequence of transformations proves that shape i is similar to shape ii?
a. a reflection across the x - axis, and then a translation 6 units right
b. translation 6 units right, and then a 90° clockwise rotation about the origin
c. a 180° counterclockwise rotation about the origin
d. a reflection across the y - axis, and then a translation 4 units up
e. a reflection across the x - axis, followed by a 180° counterclockwise rotation about the origin, and then a translation 4 units down

Explanation:

Step1: Analyze Option A

• Reflection across \(x -\)axis: flips shape over \(x -\)axis.
• Translation \(6\) units right: moves shape \(6\) units to the right.
• This sequence will map shape I to shape II.

Step2: Analyze Option B

• Translation \(6\) units right: moves shape \(6\) units to the right.
• \(90^{\circ}\) clockwise rotation about origin: changes orientation in a way that won't map shape I to shape II.

Step3: Analyze Option C

• \(180^{\circ}\) counter - clockwise rotation about origin: changes orientation and position in a way that won't map shape I to shape II.

Step4: Analyze Option D

• Reflection across \(y -\)axis: flips shape over \(y -\)axis.
• Translation \(4\) units up: moves shape \(4\) units up. This won't map shape I to shape II.

Step5: Analyze Option E

• Reflection across \(x -\)axis: flips shape over \(x -\)axis.
• \(180^{\circ}\) counter - clockwise rotation about origin: further changes orientation.
• Translation \(4\) units down: moves shape \(4\) units down. This won't map shape I to shape II.

Answer:

A. a reflection across the \(x -\)axis, and then a translation \(6\) units right