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use betweenness of points to answer this question.

If points F, G, and H are collinear and if FG= 5, FH= 8, and GH= 13, which point is between the other two?

1 answer

To determine which point is between the other two, we can use the information about the distances given.

Let's denote:

  • FG = 5 (the distance between points F and G)
  • FH = 8 (the distance between points F and H)
  • GH = 13 (the distance between points G and H)

According to the concept of betweenness of points, if one point is between two others, the sum of the distances from one point to the other two should equal the distance between the outer points.

Let's check the combinations:

  1. Assuming G is between F and H:

    • FG + GH = 5 + 13 = 18
    • FH = 8 This does not hold true.

  2. Assuming F is between G and H:

    • FG + FH = 5 + 8 = 13
    • GH = 13 This holds true.

  3. Assuming H is between F and G:

    • FH + GH = 8 + 13 = 21
    • FG = 5 This does not hold true.

Since only the second assumption (that F is between G and H) holds true, we conclude that point F is between points G and H.