Question

select the sequence of transformations that will carry triangle a onto triangle a.
a reflect over x - axis, then 12 units right
b translate 12 units right, then reflect over x - axis
c rotate 90° clockwise, reflect over x - axis, then translate 12 units right
d reflect over y - axis, translate 4 units right, then translate 10 units down

Explanation:

Step1: Analyze option A

• Reflect triangle A over the \(x -\)axis: This flips the triangle vertically.
• Then translate 12 units right: Moving the reflected triangle 12 units to the right.

Step2: Analyze option B

• Translate 12 units right first: If we translate first, the orientation (due to reflection later) will not match as expected.

Step3: Analyze option C

• Rotate \(90^{\circ}\) clockwise: This changes the orientation of the triangle in a way that is not needed.

Step4: Analyze option D

• Reflect over \(y -\)axis: This flips the triangle horizontally in an incorrect way.

Answer:

A. reflect over x - axis, then 12 units right