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In the provided image, we see a diagram involving points \( A \) and \( B \), and a perpendicular bisector labeled as line \( l \), intersecting the segment \( AB \). The problem asks whether point \( C \) is closer to point \( A \), closer to point \( B \), or equidistant from both points.

### Explanation:
When a point lies on the perpendicular bisector of a segment, it is equidistant from both endpoints of the segment. This is a key property of the perpendicular bisector. Since point \( C \) lies on line \( l \), the perpendicular bisector of segment \( AB \), it must be the same distance from both points \( A \) and \( B \).

Thus, **the correct answer is: "Point C is the same distance between points A and B."**

Would you like more details or have any other questions?

Here are five related questions for further exploration:
1. How do you find the equation of the perpendicular bisector of a line segment?
2. What are some applications of perpendicular bisectors in geometry?
3. How can you prove that a point is equidistant from two other points?
4. How does the concept of perpendicular bisectors apply in the construction of circumcircles?
5. Can a point on a perpendicular bisector also be closer to one of the endpoints under certain conditions?

**Tip:** The perpendicular bisector of a line segment not only divides the segment into two equal halves but also forms a 90-degree angle with the segment.

In the diagram, is point C closer to point A, closer to point B, or the same distance between the points?

In this problem, learn how to determine whether point C is equidistant from points A and B based on the geometric property of a perpendicular bisector. Suitable for students in Grades 6-8, the problem explores the perpendicular bisector theorem.

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