Question

1. on the set of axes below, triangle abc is graphed. triangles abc and abc, the images of triangle abc, are graphed after a sequence of rigid motions. identify which sequence of rigid motions maps △abc onto △abc and then maps △abc onto △abc. a) a reflection followed by a rotation b) a rotation followed by another rotation c) a translation followed by a reflection d) a reflection followed by a translation

Explanation:

Step1: Analyze the transformation from $\triangle ABC$ to $\triangle A'B'C'$

• Rigid motions include translation, rotation, and reflection.
• Observe the orientation of $\triangle ABC$ and $\triangle A'B'C'$. The orientation is reversed (mirror - like). So, the transformation from $\triangle ABC$ to $\triangle A'B'C'$ is a reflection.

Step2: Analyze the transformation from $\triangle A'B'C'$ to $\triangle A''B''C''$

• Observe the position of $\triangle A'B'C'$ and $\triangle A''B''C''$. The shape and orientation (after reflection) of $\triangle A'B'C'$ and $\triangle A''B''C''$ are the same, but their positions are different. A translation (a slide) moves a figure without rotating or reflecting it. The transformation from $\triangle A'B'C'$ to $\triangle A''B''C''$ is a translation.

Answer:

D. a reflection followed by a translation