Question

select the sequence of transformations that will carry rectangle a onto rectangle a.
a reflect over y - axis, rotate 90° clockwise, then reflect over x - axis
b rotate 180° clockwise, reflect over y - axis, then translate 3 units left
c rotate 180° clockwise, reflect over x - axis, then translate 2 units left
d rotate 90° clockwise, reflect over y axis, then translate 3 units left

Explanation:

Step1: Analyze Option A

• Reflect over \(y\) - axis: Changes the \(x\) - coordinate sign.
• Rotate \(90^{\circ}\) clockwise: \((x,y)\to(y, - x)\).
• Reflect over \(x\) - axis: Changes the \(y\) - coordinate sign. This sequence does not map rectangle \(A\) to \(A'\).

Step2: Analyze Option B

• Rotate \(180^{\circ}\) clockwise: \((x,y)\to(-x,-y)\).
• Reflect over \(y\) - axis: \((x,y)\to(-x,y)\).
• Translate 3 units left: \((x,y)\to(x - 3,y)\). This sequence maps rectangle \(A\) to \(A'\).

Step3: Analyze Option C

• Rotate \(180^{\circ}\) clockwise: \((x,y)\to(-x,-y)\).
• Reflect over \(x\) - axis: \((x,y)\to(x,-y)\).
• Translate 2 units left: \((x,y)\to(x - 2,y)\). This sequence does not map rectangle \(A\) to \(A'\).

Step4: Analyze Option D

• Rotate \(90^{\circ}\) clockwise: \((x,y)\to(y, - x)\).
• Reflect over \(y\) - axis: \((x,y)\to(-x,y)\).
• Translate 3 units left: \((x,y)\to(x - 3,y)\). This sequence does not map rectangle \(A\) to \(A'\).

Answer:

B. rotate \(180^{\circ}\) clockwise, reflect over \(y\) - axis, then translate 3 units left