### Video Transcript

What is the projection of the line segment between π΄ and π΅ on the line passing through π΅ and πΆ?

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 π΅ lies on the line between π΅ and πΆ. So π΅ is its own projection onto the line. This means that we need to find the projection of π΄ onto the line.

We can recall that this is the point π΄ prime that lies on the line passing through π΅ and πΆ such that the line segment between π΄ and π΄ prime is perpendicular to the line passing through π΅ and πΆ. To find the projection of π΄, letβs highlight the line segment and straight line on the given figure. Remember, the line passing through π΅ and πΆ extends indefinitely in both directions. We can then note that the line segment between π΄ and π is perpendicular to the line passing through π΅ and πΆ, and π lies on the line. Hence, π is the projection of π΄ on the line passing through π΅ and πΆ.

We can then conclude that the projection of the line segment between π΄ and π΅ onto the line passing through π΅ and πΆ is the line segment between π and π΅.