Question

based on the image, what transformation maps triangle abc to triangle abc?rotation 90° clockwisetranslation 4 units leftreflection across the y - axis

Explanation:

Step1: Recall reflection rule

Reflection across the \(y -\)axis: \((x,y)\to(-x,y)\).

Step2: Check coordinates

Assume a point \(P(x,y)\) on \(\triangle ABC\). After reflection across \(y -\)axis, it becomes \(P'(-x,y)\). Visually, the two triangles are mirror - images about the \(y -\)axis.

Step3: Eliminate other options

• Rotation \(90^{\circ}\) clockwise: \((x,y)\to(y, - x)\), which changes the orientation more than just mirroring.
• Translation \(4\) units left: \((x,y)\to(x - 4,y)\), but the distance from \(y -\)axis for corresponding points is same (not shifted left - right by \(4\) units in a translation sense here as per reflection property).

Answer:

Reflection across the \(y -\)axis.