Question

if gregory draws the segment with endpoints b and c, then the midpoint will be on the line of reflection. points a and b are equidistant from the line of reflection. if gregory draws the segment with endpoints a and a, then the midpoint will lie on the line of reflection. ab will be perpendicular to the line of reflection.

Explanation:

Step1: Recall the property of reflection

When a figure is reflected over a line, the line of reflection is the perpendicular bisector of the segment joining a point and its image.

Step2: Analyze each option

• For the segment with endpoints \(B\) and \(C'\): The line of reflection is the perpendicular bisector of the segment joining a point and its image. The mid - point of the segment with endpoints \(B\) and \(C'\) is on the line of reflection.
• For the segment with endpoints \(A\) and \(A'\): The mid - point of the segment with endpoints \(A\) and \(A'\) lies on the line of reflection.
• For \(\overline{AB}\): \(\overline{AB}\) is not necessarily perpendicular to the line of reflection.

Answer:

If Gregory draws the segment with endpoints \(B\) and \(C'\), then the midpoint will be on the line of reflection.