Let's match the teacher's comments to the students' definitions of a line segment:
1. Ivy's definition:
"All of the points in line with [tex]\(P\)[/tex] and [tex]\(Q\)[/tex], extending infinitely in both directions."
Teacher's comment: "Are you thinking of a line instead of a line segment?"
Explanation: Ivy described a line, which extends infinitely in both directions. A line segment, however, has two endpoints and does not extend infinitely.
2. Ethan's definition:
"The exact distance from [tex]\(P\)[/tex] to [tex]\(Q\)[/tex]."
Teacher's comment: "Not quite. There's more to a segment than just how long it is."
Explanation: Ethan focused only on the distance between [tex]\(P\)[/tex] and [tex]\(Q\)[/tex], which is the length of the segment, but did not mention the segment's endpoints or the points in between.
3. Ebuka's definition:
"The points [tex]\(P\)[/tex] and [tex]\(Q\)[/tex], which are called endpoints, and all of the points in a straight line between points [tex]\(P\)[/tex] and [tex]\(Q\)[/tex]."
Teacher's comment: "Kudos! You are correct."
Explanation: Ebuka provided a complete and correct definition of a line segment, which includes the endpoints [tex]\(P\)[/tex] and [tex]\(Q\)[/tex] and all points in between.
So, the correct matching is:
- Ivy's definition: Are you thinking of a line instead of a line segment?
- Ethan's definition: Not quite. There's more to a segment than just how long it is.
- Ebuka's definition: Kudos! You are correct.
