Question

the diagrams show a polygon and the image of the polygon after a transformation. three diagrams are labeled from left to right: rotation, translation, reflection. the x - and y - axes are labeled. use the diagrams to determine which statements are true. select all statements that are true. parallel lines will never be parallel after a rotation. parallel lines will always be parallel after a reflection. parallel lines will sometimes not be parallel after a translation. lines that are not parallel will always be parallel after a rotation.

Explanation:

Step1: Understand transformation properties

Reflection is a rigid - motion that preserves distance and angle measures.

Step2: Analyze parallel lines and reflection

If two lines are parallel, their slopes are equal. A reflection does not change the slope of lines. So, parallel lines remain parallel after reflection.

Step3: Analyze parallel lines and rotation

A rotation can change the orientation of lines. Non - parallel lines can become parallel and vice - versa after rotation. So, parallel lines will not always be parallel after rotation.

Step4: Analyze parallel lines and translation

Translation is a rigid - motion that moves every point of a figure the same distance in the same direction. Parallel lines will always be parallel after translation. But the question asks for statements about rotation, reflection. So we focus on reflection here.

Answer:

Parallel lines will always be parallel after a reflection.