Question

consider these four statements about a line that passes through two points on a plane.
statement a: the line is on a different plane from the points.
statement b: the line lies on only one plane.
statement c: the line is on the same plane as the points.
statement d: the line passes through only one plane.
only statement

is true.
type the correct answer in the box. spell all words correctly.

Explanation:

According to the axiom of plane - line relations in geometry, if two points are on a plane, then the line passing through these two points is on the same plane. So statement C is correct. Statement A is wrong because the line is on the same plane as the points. Statement B is wrong because the line is on the plane (not lies on only one plane in the sense of being restricted to a single plane when there is a plane containing it). Statement D is wrong because the line passes through two points on a plane and is on that plane (not passing through only one plane in an incorrect sense).

Answer:

Statement C