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Three students attempt to define what a line segment is. Can you match the teacher's comments to the definitions?

[tex]\[
\begin{tabular}{|c|c|}
\hline
Definition of a line segment & Teacher's comments \\
\hline
\begin{tabular}{l}
Ivy's definition: All of the points in line with \\
$P$ and $Q$, extending infinitely in both \\
directions.
\end{tabular}
&
\begin{tabular}{l}
Are you thinking of a \\
line instead of a line \\
segment?
\end{tabular} \\
\hline
\begin{tabular}{l}
Ethan's definition: The exact distance from \\
$P$ to $Q$.
\end{tabular}
&
Kudos! You are correct. \\
\hline
\begin{tabular}{l}
Ebuka's definition: The points $P$ and $Q$, \\
which are called endpoints, and all of the \\
points in a straight line between points $P$ \\
and $Q$.
\end{tabular}
&
\begin{tabular}{l}
Not quite. There's more \\
to a segment than just \\
how long it is.
\end{tabular} \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnsweridn
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.
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