Let's address the question step-by-step:
1. Understanding the Perpendicular Bisector:
- A perpendicular bisector of a line segment is a line that divides the segment into two equal parts at a 90-degree angle.
- In our scenario, PQ is the line segment connecting points P and Q.
2. Properties of the Perpendicular Bisector:
- By definition, any point on the perpendicular bisector of a line segment PQ is equidistant from P and Q.
- Equidistant means the distance from any point on the bisector to P is the same as the distance from that point to Q.
3. Application:
- If you pick any point on the perpendicular bisector, and measure the distance to P and the distance to Q, you will find that these distances are equal.
- Conversely, if you find a point that is equidistant from both P and Q, it must lie on the perpendicular bisector of PQ.
4. Conclusion:
- The perpendicular bisector of PQ is indeed the set of all points that are equidistant from P and Q.
Therefore, the statement "the perpendicular bisector of PQ is the set of all points equidistant from P and Q" is:
A. True
