Question Video: Finding the Intersection between a Line Segment and a Plane Mathematics

Video Transcript

What is the intersection between segment 𝐵𝐵 dash and the plane 𝐴𝐵𝐶?

Well let’s first consider the plane 𝐴𝐵𝐶. This has three vertices 𝐴, 𝐵, and 𝐶 and three edges or line segments 𝐴𝐵, 𝐵𝐶, and 𝐶𝐴. Now let’s consider the line segment or edge 𝐵𝐵 dash.

This has two vertices 𝐵 and 𝐵 dash and has just one line from 𝐵 to 𝐵 dash. Does this line segment intersect the plane at a vertex or at an edge?

Well the only points of intersection between the segment and the plane is at the vertex or point 𝐵. Therefore, the intersection is 𝐵.

We can write this as 𝐵𝐵 dash intersects 𝐴𝐵𝐶 at 𝐵. The only point or vertex that appears in both parts of the question is point 𝐵.