Question

describe the sequence of rigid motions that was used to take each vertex of triangle abc onto the corresponding vertex of triangle def.
translate triangle abc by the directed line segment. then rotate the resulting image by angle counterclockwise around point. then reflect the resulting image across segment.

Explanation:

Step1: Analyze translation

To translate triangle \(ABC\) to a new position, we look at the movement from \(A\) to \(A'\). The directed line segment is \(AA'\).

Step2: Analyze rotation

After translation, we need to rotate the triangle. By observing the orientation change, the rotation is \(90^{\circ}\) counter - clockwise around point \(E\).

Step3: Analyze reflection

After rotation, to map the triangle to \(DEF\), we reflect the resulting image across segment \(EF\).

Answer:

Translate triangle \(ABC\) by the directed line segment \(AA'\). Then rotate the resulting image by angle \(90^{\circ}\) counterclockwise around point \(E\). Then reflect the resulting image across segment \(EF\).