Video Transcript
What is the projection of π· on
line π΄πΆ?
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, thatβs the line
π΄πΆ. We say that π΄πΆ is our target
line, and we want to project the point π· 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 πΈπ· is perpendicular to the line π΄πΆ. If we imagine this perpendicular
line as a light source, the projection of π· onto π΄πΆ will be the shadow of π· onto
line π΄πΆ. And the shadow of this point will
be another point. In this case, itβs going to be the
point πΈ. The point πΈ is the place of the
intersection of the perpendicular line π·πΈ onto π΄πΆ.
And so, we can call the point πΈ
the projection.
