Video: Identifying the Projection of a Point

What is the projection of 𝐷 on line 𝐴𝐢?


Video Transcript

What is the projection of 𝐷 on line 𝐴𝐢?

When we think about projections, the first thing we wanna identify is our target line, the line on which our projection will fall. In this case, that’s the line 𝐴𝐢. We say that 𝐴𝐢 is our target line, and we want to project the point 𝐷 onto this target line. To do that, we need to consider a perpendicular line to our target line that intersects the point we want to make a projection of.

Helpfully, we see here that line segment 𝐸𝐷 is perpendicular to the line 𝐴𝐢. If we imagine this perpendicular line as a light source, the projection of 𝐷 onto 𝐴𝐢 will be the shadow of 𝐷 onto line 𝐴𝐢. And the shadow of this point will be another point. In this case, it’s going to be the point 𝐸. The point 𝐸 is the place of the intersection of the perpendicular line 𝐷𝐸 onto 𝐴𝐢.

And so, we can call the point 𝐸 the projection.

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