Question

three students attempt to define what a circle is. can you match the teachers comments to the definitions? definition of a circle teacher’s comments durus definition: the set of all points in a plane that are the same distance away from some given point, which we call the center. your definition needs to be much more precise. olivers definition: the set of all points in 3d space that are the same distance from a center point. you seem to be confusing a circle with a sphere. carloss definition: a perfectly round shape. stupendous! well done.

Explanation:

• Duru's definition: A circle is a 2D figure (set of points in a plane) with all points equidistant from a center. This is the correct mathematical definition, so the teacher's comment "Stupendous! Well done." matches Duru.
• Oliver's definition: A circle is in a plane (2D), but Oliver mentions 3D space. A sphere is the set of points in 3D space equidistant from a center, so the comment "You seem to be confusing a circle with a sphere." matches Oliver.
• Carlos's definition: "A perfectly round shape" is too vague (e.g., a sphere is also round). So the comment "Your definition needs to be much more precise." matches Carlos.

Answer:

• Duru's definition: Stupendous! Well done.
• Oliver's definition: You seem to be confusing a circle with a sphere.
• Carlos's definition: Your definition needs to be much more precise.