Video: Identifying the Projection of Perpendicular Line Segments

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

01:27

Video Transcript

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

When we’re working with these kind of projections, we always want to consider the target line first, the line on which the projection will fall. In this case, it’s the line 𝐡𝐢, so we’ll show that line 𝐡𝐢 is our target line. The segment we’re using that we want to project is 𝐴𝐷, this segment. We should be noticing that our line segment we want to make projection of is perpendicular to our target line. When we try to visualize a projection, we always use lines that are perpendicular to the target line. So how do we visualize line segment 𝐴𝐷?

Imagine that we have a laser light source where it’s shining a light perpendicular to our line 𝐡𝐢. What kind of shadow is it going to create? Well, when it hits point 𝐴, it’s just going to make a point as a projection. Its shadow will just be the point 𝐷. We might be able to visualize this a bit better if we take it out of the triangle. Once our light source hits point 𝐴, its shadow will just be a point. It will not be a line segment. And so the projection of line segment 𝐴𝐷 onto the line 𝐡𝐢 is the point 𝐷.

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