Question Video: Knowing the Number of Planes That Can Pass through Noncollinear Points Mathematics • 11th Grade

How many planes can pass through three non-colinear points?


Video Transcript

How many planes can pass through three noncolinear points?

Imagine that we have three arbitrary points in space 𝐴, 𝐵, and 𝐶. We know that between any two points, there exists only one line, which means one line passes through the point 𝐴𝐵; one line could pass through the point 𝐴𝐶, which would create a set of intersecting lines. And if there wasn’t a line passing from the point 𝐴𝐶, if the line through 𝐶 is parallel to the line 𝐴𝐵, it is still true that 𝐴, 𝐵, and 𝐶 are noncolinear. They’re not on the same line. But parallel lines in space and intersecting lines in space are coplanar; they exist on the same plane. And this means that through any three non colinear points, there will be exactly one plane.

Based on the properties of points, lines, and planes in space, we can say that there exists exactly one plane through any three noncolinear points.

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