Video Transcript
What is the projection of line
segment 𝐴𝐷 onto line 𝐵𝐶?
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 𝐵𝐶,
so we’ll show that line 𝐵𝐶 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 𝐵𝐶. 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 𝐵𝐶 is the point 𝐷.
