Question

in a geometry class, students are asked to describe the dimensions of a plane based on the components that create a plane. which student’s response is correct?
mark states that a plane has zero dimensions because it is made up of three noncollinear points.
stacy states that a plane has two dimensions because it is made up of an infinite number of lines.
dewayne states that a plane has one dimension because it contains the line intersecting two points.
candice states that a plane can have multiple dimensions depending on how many points are labeled.

Explanation:

• Analyze Mark's response: A plane is not zero - dimensional. Three non - collinear points define a plane, but a plane extends infinitely in two directions. So Mark is wrong.
• Analyze Stacy's response: A plane is a two - dimensional figure. A line is one - dimensional, and a plane can be thought of as being composed of an infinite number of lines (extending in two directions), so a plane has two dimensions. This is correct.
• Analyze Dewayne's response: A line is one - dimensional, but a plane contains many lines and is two - dimensional, not one - dimensional. So Dewayne is wrong.
• Analyze Candice's response: The number of labeled points does not change the fact that a plane is inherently two - dimensional. So Candice is wrong.

Answer:

Stacy states that a plane has two dimensions because it is made up of an infinite number of lines.