Video: Determining the Point That Bisects a Line Segment between Two Given Points on a Number Line

Point 𝐷 bisects the segment between 𝐴 and 𝐵. What number is 𝐷 at?

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Video Transcript

Point 𝐷 bisects the segment between 𝐴 and 𝐵. What number is 𝐷 at?

We can see from the number line that point 𝐴 is at two and point 𝐵 is at six. If point 𝐷 bisects these points, it must be halfway between them. It is the midpoint of 𝐴 and 𝐵. We can see from the number line that there are four jumps from two to six. One-half of four is equal to two. Moving two spaces to the right of 𝐴 gets us to four as two plus two equals four. Moving two places to the left of 𝐵 also gets us to four as six minus two equals four.

The value of 𝐷, which is the midpoint of 𝐴 and 𝐵, is four. If the numbers were further apart, then using a number line might not be practical. To find the midpoint of any two numbers, 𝑥 and 𝑦, we add the two numbers and divide by two. In this case, we add two and six and then divide the answer by two. Two plus six is equal to eight and a half of eight or eight divided by two is four. This proves that if point 𝐷 bisects the segment between 𝐴 and 𝐵, then the number that 𝐷 is at is four.

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