in the diagram of collinear points, GK = 24, HJ = 10, and GH=HI=IJ. Find each length.

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5. HI

Solve it

To find the lengths of the segments GH, HI, and IJ in the diagram of collinear points, we can use the information given.

We know that GH = HI = IJ because the points G, H, I, and J are collinear. Let's assume that the length of GH, HI, and IJ is x.

From the information given, we know that GK = 24 and HJ = 10. So, we can write the following equations:

GH + HI + IJ = GK + KJ (by substituting the collinear segments)
x + x + x = 24 + 10 (substituting the value of each segment)
3x = 34 (adding the lengths on both sides)
x = 34/3 (dividing both sides by 3)
x ≈ 11.33

Therefore, the length of each segment would be approximately 11.33 (or rounded to an appropriate decimal place). So, GH ≈ 11.33, HI ≈ 11.33, and IJ ≈ 11.33.