Video Transcript
What is the result of projecting a point onto a straight line?
In this question, we are asked to determine the result of projecting a point onto a straight line. To do this, let’s recall the definition of this projection.
If a point 𝐴 lies on the line passing through 𝐵 and 𝐶, then the projection of 𝐴 onto the line is the point 𝐴 itself. Otherwise, we want the point 𝐴 prime on the line such that the line passing through 𝐴 and 𝐴 prime is perpendicular to the line passing through 𝐵 and 𝐶. In both cases, we can see that the result of this projection is a point. This is enough to answer the question. However, it can be useful to see this graphically.
Let’s say that we have the following line passing through 𝐵 and 𝐶 and a point 𝐴 that is not on the line. Then, the projection of 𝐴 onto the line is the point 𝐴 prime on the line such that the line segment between 𝐴 and 𝐴 prime is perpendicular to the line as shown. We have a similar story if we want to project a point on the line onto the line, say point 𝐷. In this case, the projection of 𝐷 is just 𝐷 itself. In either case, we can see that the projection of a point onto a line is a point.
