Video: Identifying the Projection of a Line Segment on a Straight Line

What is the projection of line segment 𝐴𝐷 on line 𝐴𝐢?

01:20

Video Transcript

What is the projection of line segment 𝐴𝐷 onto line 𝐴𝐢?

First of all, we want to know what our target line is. This is the line on which our projection will fall. Since we want to know the projection of line segment 𝐴𝐷 onto line 𝐴𝐢, line 𝐴𝐢 is our target line. First, we identify line 𝐴𝐢, and then we need the segment that we want to make a projection of, which is 𝐴𝐷. To visualize a projection, we need to visualize a light source that is perpendicular to our target line. In this diagram, we already have a line segment that’s perpendicular to our target line. That’s the line segment 𝐷𝑀. We’ll use lines that are parallel to 𝐷𝑀 to find this projection.

If we want to know what kind of shadow this line segment 𝐴𝐷 would create, it would fall between 𝐴 and 𝑀 on our target line, with the line segment 𝐴𝑀 being its shadow. That shadow portion is the projection. And so we say that the projection of line segment 𝐴𝐷 onto line 𝐴𝐢 would be line segment 𝐴𝑀.

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