### Video Transcript

What is the result of projecting a line segment onto a straight line, given that the two are not perpendicular?

In this question, we need to determine the result of projecting a line segment onto a straight line using the fact that the two are not perpendicular. To answer this question, we first need to recall how we project a line segment onto a line. And we will do this by recalling the definition of projecting a point onto a line.

We recall that the projection of a point 𝑃 onto the line passing through 𝐴 and 𝐵 is the point 𝑃 if 𝑃 lies on the line. And this is the point 𝑃 prime such that 𝑃 prime lies on the line. And the line segment between 𝑃 and 𝑃 prime is perpendicular to the line passing through 𝐴 and 𝐵 if 𝑃 does not lie on the line.

We can then recall that we project a line segment onto a line by projecting every point of the line segment onto the line. For instance, consider the following nonperpendicular line segment and line. We can project 𝑃 onto the line by drawing a perpendicular line to 𝐴𝐵 that passes through 𝑃. We can follow this same process for any point on the line segment. For instance, we can find that the projection of 𝑄 is as shown. We see that the projection of all of the points together is the line segment between 𝑃 prime and 𝑄 prime.

In general, we have that the projection of a line segment onto a line is found by projecting the endpoints of the line segment onto the line. There is one thing worth noting about this definition, which is that if the line segment is perpendicular to the line, the projection of the endpoints are coincident, leaving us with a single point. However, in this question, they are not perpendicular. So we must obtain a line segment.