Question

three students attempt to define what a line segment is.
can you match the teachers comments to the definitions?

definition of a line segment | teachers comments
--- | ---
rubys definition: two points, call them end points, and all of the other points in a straight line between them. | were you thinking of a circle or perhaps a sphere?
shriyas definition: a line between two points. | your definition is kind of correct, but it lacks mathematical precision.
abhisheks definition: all of the points equidistant from some point p. | wunderbar! well done.

Explanation:

Step1: Analyze Ruby's Definition

Ruby's definition: "Two points, call them end points, and all of the other points in a straight line between them." This is the correct definition of a line segment. So the teacher's comment "Wunderbar! Well done." should match Ruby's definition.

Step2: Analyze Shriya's Definition

Shriya's definition: "A line between two points." This is a vague definition (a line between two points could be a line segment, but the definition lacks precision like not mentioning it's the set of points between the two endpoints). So the comment "Your definition is kind of correct, but it lacks mathematical precision." matches Shriya's definition.

Step3: Analyze Abhishek's Definition

Abhishek's definition: "All of the points equidistant from some point \( P \)." This is the definition of a circle (or sphere in 3D), not a line segment. So the comment "Were you thinking of a circle or perhaps a sphere?" matches Abhishek's definition.

Answer:

• Ruby's definition ↔ "Wunderbar! Well done."
• Shriya's definition ↔ "Your definition is kind of correct, but it lacks mathematical precision."
• Abhishek's definition ↔ "Were you thinking of a circle or perhaps a sphere?"