Question

1. choose the best answer. which point is the midpoint of a line segment? a x z y

Explanation:

Step1: Recall the definition of midpoint

A midpoint of a line segment is a point that divides the segment into two congruent (equal - length) parts. Given that \(\overline{AY}\cong\overline{YC}\), we need to check which point satisfies this condition.

Step2: Analyze each point

• Point \(A\): It is one of the endpoints of the segment \(\overline{AC}\) (assuming the segment is between \(A\) and \(C\) based on the congruence \(\overline{AY}\cong\overline{YC}\)), so it cannot be the midpoint.
• Point \(X\): It is on a different line (the vertical line) and has no relation to the congruence \(\overline{AY}\cong\overline{YC}\) for the horizontal line segment.
• Point \(Z\): It is on a different line (the vertical line) and has no relation to the congruence \(\overline{AY}\cong\overline{YC}\) for the horizontal line segment.
• Point \(Y\): Since \(\overline{AY}\cong\overline{YC}\), by the definition of a midpoint (a point \(M\) of a segment \(\overline{AB}\) such that \(\overline{AM}\cong\overline{MB}\)), when the segment is \(\overline{AC}\) and \(\overline{AY}\cong\overline{YC}\), \(Y\) is the midpoint of the line segment \(\overline{AC}\).

Answer:

\(Y\)