Question

three students attempt to define what a circle is.
can you match the teachers comments to the definitions?
ivys definition: a 2d geometric shape that is both round and closed, having no corners.
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.
ebukas definition: a 2 - dimensional shape made by drawing a curve that is always the same distance from a center.
teachers comments
your definition is close, but it isnt precise enough. a half - circle, for example, would also fit your definition.
correct! your definition is very clear and precise.
sorry, this is incorrect. an ellipse, for example, would also fit your definition.

Explanation:

• Ivy's definition: A half - circle is also round, closed, 2D and has no corners. So the comment "Your definition is close, but it isn't precise enough. A half - circle, for example, would also fit your definition." matches Ivy's definition.
• Ethan's definition: This is the standard mathematical definition of a circle (in a plane) using the center \(C\) and radius \(r\). So the comment "Correct! Your definition is very clear and precise." matches Ethan's definition.
• Ebuka's definition: An ellipse has a center and a curve where points are at a constant sum of distances from two foci (in a sense, can be thought of as a "center - like" property in some definitions related to its symmetry center), so the comment "Sorry, this is incorrect. An ellipse, for example, would also fit your definition." matches Ebuka's definition.

Answer:

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