Select the choice that indicates PQ is the perpendicular bisector of XY if they intersect at M

Answer 1

For line segment PQ to be the perpendicular bisector of line segment XY at point M, the following conditions must be satisfied:

1. Midpoint Condition: M must be the midpoint of XY. This means that XM = MY, where X and Y are the endpoints of the line segment XY.

2. Perpendicular Condition: PQ must intersect XY at point M at a right angle (90 degrees). This means that the angle formed by lines PQ and XY at point M is a right angle.

If you need to express these conditions formally, you could write:

• \( M = \frac{X + Y}{2} \) (Midpoint)
• \( PQ \perp XY \) at M (Perpendicular)

So, the choice should clearly indicate that both the midpoint condition and the perpendicular condition hold true at point M. If you have choices provided in a question format, look for one that encapsulates these two points.