Question Video: Identifying Projections of Line Segments Mathematics • Second Year of Preparatory School

Video Transcript

What is the projection of the line segment between 𝐴 and 𝐵 on the line passing through 𝐵 and 𝐶?

In this question, we are asked to find the projection of a line segment onto a line using a given figure. We can start by recalling that we project a line segment onto a line by finding the line segment between the projection of the endpoints. We can also note that 𝐵 lies on the line between 𝐵 and 𝐶. So 𝐵 is its own projection onto the line. This means that we need to find the projection of 𝐴 onto the line.

We can recall that this is the point 𝐴 prime that lies on the line passing through 𝐵 and 𝐶 such that the line segment between 𝐴 and 𝐴 prime is perpendicular to the line passing through 𝐵 and 𝐶. To find the projection of 𝐴, let’s highlight the line segment and straight line on the given figure. Remember, the line passing through 𝐵 and 𝐶 extends indefinitely in both directions. We can then note that the line segment between 𝐴 and 𝑋 is perpendicular to the line passing through 𝐵 and 𝐶, and 𝑋 lies on the line. Hence, 𝑋 is the projection of 𝐴 on the line passing through 𝐵 and 𝐶.

We can then conclude that the projection of the line segment between 𝐴 and 𝐵 onto the line passing through 𝐵 and 𝐶 is the line segment between 𝑋 and 𝐵.