Video Transcript
What is the projection of line
segment ๐ด๐ท onto line ๐ต๐ถ?
When weโre 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, itโs the line ๐ต๐ถ,
so weโll show that line ๐ต๐ถ is our target line. The segment weโre using that we
want to project is ๐ด๐ท, 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
๐ด๐ท?
Imagine that we have a laser light
source where itโs shining a light perpendicular to our line ๐ต๐ถ. What kind of shadow is it going to
create? Well, when it hits point ๐ด, itโs
just going to make a point as a projection. Its shadow will just be the point
๐ท. We might be able to visualize this
a bit better if we take it out of the triangle. Once our light source hits point
๐ด, its shadow will just be a point. It will not be a line segment. And so the projection of line
segment ๐ด๐ท onto the line ๐ต๐ถ is the point ๐ท.
