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Sagot :
Sure, let's analyze the three definitions step by step and match them with the teacher's comments appropriately.
### Definitions:
1. Ruby's Definition:
- Text: "Two points, call them end points, and all of the other points in a straight line between them."
- Analysis: Ruby's definition captures the essential idea of a line segment, involving two end points and the points in a straight line between them. However, it may be seen as lacking some formal mathematical terms, thus it is not fully precise.
- Teacher's Comment: "Your definition is kind of correct, but it lacks mathematical precision."
2. Shriya's Definition:
- Text: "A line between two points."
- Analysis: While very concise, it adequately describes a line segment. It’s clear and captures the essence of a line segment succinctly.
- Teacher's Comment: "Wunderbar! Well done."
3. Abhishek's Definition:
- Text: "All of the points equidistant from some point [tex]\(P\)[/tex]."
- Analysis: This definition is describing a collection of points that are all at the same distance from a single point [tex]\(P\)[/tex]. This describes a circle (or a sphere in three dimensions), not a line segment.
- Teacher's Comment: "Were you thinking of a circle or perhaps a sphere?"
### Matching Definitions to Comments:
1. Ruby's Definition receives the comment: "Your definition is kind of correct, but it lacks mathematical precision."
2. Shriya's Definition receives the comment: "Wunderbar! Well done."
3. Abhishek's Definition receives the comment: "Were you thinking of a circle or perhaps a sphere?"
### Final Solution:
\begin{tabular}{c|c}
Definition of a line segment & Teacher's comments \\
\hline
\begin{tabular}{c}
Ruby's definition: Two points, call them \\
end points, and all of the other points in \\
a straight line between them.
\end{tabular} & \begin{tabular}{c}
Your definition is kind of \\
correct, but it lacks \\
mathematical precision.
\end{tabular} \\
\begin{tabular}{c}
Shriya's definition: A line between two \\
points.
\end{tabular} & Wunderbar! Well done. \\
\begin{tabular}{c}
Abhishek's definition: All of the points \\
equidistant from some point [tex]$P$[/tex].
\end{tabular} & \begin{tabular}{l}
Were you thinking of a circle \\
or perhaps a sphere?
\end{tabular} \\
\hline
\end{tabular}
### Definitions:
1. Ruby's Definition:
- Text: "Two points, call them end points, and all of the other points in a straight line between them."
- Analysis: Ruby's definition captures the essential idea of a line segment, involving two end points and the points in a straight line between them. However, it may be seen as lacking some formal mathematical terms, thus it is not fully precise.
- Teacher's Comment: "Your definition is kind of correct, but it lacks mathematical precision."
2. Shriya's Definition:
- Text: "A line between two points."
- Analysis: While very concise, it adequately describes a line segment. It’s clear and captures the essence of a line segment succinctly.
- Teacher's Comment: "Wunderbar! Well done."
3. Abhishek's Definition:
- Text: "All of the points equidistant from some point [tex]\(P\)[/tex]."
- Analysis: This definition is describing a collection of points that are all at the same distance from a single point [tex]\(P\)[/tex]. This describes a circle (or a sphere in three dimensions), not a line segment.
- Teacher's Comment: "Were you thinking of a circle or perhaps a sphere?"
### Matching Definitions to Comments:
1. Ruby's Definition receives the comment: "Your definition is kind of correct, but it lacks mathematical precision."
2. Shriya's Definition receives the comment: "Wunderbar! Well done."
3. Abhishek's Definition receives the comment: "Were you thinking of a circle or perhaps a sphere?"
### Final Solution:
\begin{tabular}{c|c}
Definition of a line segment & Teacher's comments \\
\hline
\begin{tabular}{c}
Ruby's definition: Two points, call them \\
end points, and all of the other points in \\
a straight line between them.
\end{tabular} & \begin{tabular}{c}
Your definition is kind of \\
correct, but it lacks \\
mathematical precision.
\end{tabular} \\
\begin{tabular}{c}
Shriya's definition: A line between two \\
points.
\end{tabular} & Wunderbar! Well done. \\
\begin{tabular}{c}
Abhishek's definition: All of the points \\
equidistant from some point [tex]$P$[/tex].
\end{tabular} & \begin{tabular}{l}
Were you thinking of a circle \\
or perhaps a sphere?
\end{tabular} \\
\hline
\end{tabular}
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