Question

three students attempt to define what a circle is. can you match the teachers comments to the definitions? definition of a circle teachers comments ivys definition: a 2d geometric shape that is both round and closed, having no corners. your definition is close, but it isnt precise enough. a half - circle, for example, would also fit your definition. ethans definition: given a distance r (call it the radius), a circle is the set of all points r units away from some fixed point c (call it the center) in a plane. sorry, this is incorrect. an ellipse, for example, would also fit your definition. ebukas definition: a 2 - dimensional shape made by drawing a curve that is always the same distance from a center. correct! your definition is very clear and precise.

Explanation:

Ivy's definition is too general as a semi - circle also meets the criteria of being round, closed and having no corners. Ethan's definition is incorrect because an ellipse has points at different distances from a center in general, while his definition could be misinterpreted to include it. Ebuka's definition correctly states that a circle is a 2 - D shape with all points on the curve at the same distance from the center.

Answer:

Ivy's definition - Your definition is close, but it isn't precise enough. A half - circle, for example, would also fit your definition.
Ethan's definition - Sorry, this is incorrect. An ellipse, for example, would also fit your definition.
Ebuka's definition - Correct! Your definition is very clear and precise.