Question Video: Deciding Whether a Point in a Figure Belongs to a Line Segment or Not

Using the figure, determine whether the following is true or false: The line segment that is passing through points 𝐡 and 𝐷 is also passing through point 𝐢.

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Video Transcript

Using the given figure, determine whether the following is true or false. The line segment that is passing through points 𝐡 and 𝐷 is also passing through point 𝐢.

In order to answer this question, we’re going to need to recall what we actually mean by a line segment. A line segment is a part of a line, and that part is bounded by two distinct endpoints. We’re told that our line segment passes through points 𝐡 and 𝐷. In fact, its two endpoints, as we can see from the diagram, are 𝐡 and 𝐷. So we represent it as shown. It’s 𝐡𝐷 with a line above it.

So let’s compare point 𝐢 to points 𝐡 and 𝐷. It sits on the line passing through these points and halfway roughly between points 𝐡 and 𝐷, halfway between the endpoints of the line segment. By definition, a line segment must be straight and contain every point on the line between its endpoints. So we can say this is true. The line segment 𝐡𝐷 passes through point 𝐢.

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