Question

on the set of axes below, triangle abc is graphed in green. triangle abc is in red and abc is in blue. identify which sequence of rigid motions maps abc onto abc and then maps abc onto abc. a reflection over the x - axis followed by a reflection over the y - axis a translation followed by a reflection over the y - axis a rotation followed by another rotation a rotation followed by a reflection across the x - axis

Explanation:

Step1: Analyze the first transformation (from \(ABC\) to \(A'B'C'\))

• Rigid motions include reflections, translations, and rotations.
• Observe the orientation and position change. A rotation can change the orientation of the triangle. Let's assume a rotation of \(180^{\circ}\) (using the property that \((x,y)\) rotated \(180^{\circ}\) about the origin becomes \((-x, -y)\)).

Step2: Analyze the second transformation (from \(A'B'C'\) to \(A''B''C''\))

• After the rotation (first step), then check the reflection. A reflection across the \(x -\)axis changes \((x,y)\) to \((x,-y)\).

Answer:

A rotation followed by a reflection across the \(x -\)axis.