Question

1. which sentence would be a good counterexample to this statement? a line can exist in only one plane. a line is parallel to one plane at a time. a line intersects one plane and then another. a line that is coplanar exists in more than one plane. a line is the intersection of two planes.

Explanation:

Step1: Analyze the statement

The statement is "A line can exist in only one plane." A counter - example should show a line exists in more than one plane.

Step2: Analyze each option

• Option "A line is parallel to one plane at a time": This does not show a line in multiple planes.
• Option "A line intersects one plane and then another": Intersecting planes is not the same as a line existing in multiple planes.
• Option "A line that is coplanar exists in more than one plane": The term "coplanar" is misused here. Coplanar means in the same plane.
• Option "A line is the intersection of two planes": If a line is the intersection of two planes, then the line lies in both planes. So it exists in more than one plane.

Answer:

A line is the intersection of two planes.