# Measuring equal distances between points on a line

I have a 36 inch piece of wood (Length) I will placing 6 coat hanger hooks along the length of the wood. The first hook will be placed 1 inch down the length from one end and the last hook will be placed 1 inch from the other end of this 36 inch piece of wood. Question how to find the equal distance between the other 4 hooks to be placed on this wood. All six hooks need to be spaced evenly.

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(34/5) inch is how far the second one needs to go from the 1st, then just continue like that. (Doesn't matter which end you start, just in case you were wondering) – Beltrame Feb 1 '12 at 19:23
the distance from the first to the last is 34in. placing four hooks will break this into 5 equal parts (draw a picture). so 34in/5=6.8in~6 and 13/16 should be the spacing between hooks(as already noted) – yoyo Feb 1 '12 at 19:27
@yoyo: How about putting that in as an answer so that it can be upvoted and the question won't be considered unanswered? – Isaac Feb 1 '12 at 20:15

You want to consider the remaining 34 inches (since you want the 1st and last to be 1inch from the edge) and divide them into 5 equal distances. This means you will need to place the 2nd hook (34/5) inches from the first and then continue in that fashion.

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If we place 1 hook at each end, we will be left with 4 hooks to place in the lenght of 34 inches. Why is the division by 5 not 4? – NoChance Feb 1 '12 at 20:25
As mentioned by yoyo, draw a picture and everything will be clear. – André Nicolas Feb 1 '12 at 21:02
@Emmad : because it s the number of intervals between the two hooks at the ends that you are concerned with. Placing 4 hooks in the middle will give you 5 of those. – Beltrame Feb 1 '12 at 21:03
Of-course, thank you all for clarification. – NoChance Feb 1 '12 at 21:22
Thank you all very much, the question is answered and is very helpful to me. The division deals with the intervals between hooks (5) and not how many hooks (4) to be placed within the 34 inches. In short I need to measure the intervals for even spacing. Visualizing this also helped.. God Bless you all. – Joe Feb 2 '12 at 13:20

It is not clear whether the question is about arithmetic, or about a practical method to be used in construction. I think it is about arithmetic, in which case Peejay's answer is exactly right. But I will answer it as a woodworker too, as this also contains mathematical ideas. Don't measure anything. Use "dividers" (the tool by that name) if you have them, otherwise take a scrap of paper and mark two points at the edge which you guess might be near the right spacing. Them move the paper along the wood, lightly marking the tentative positions, and of course you will come out too far to the left or right for hook number 6. Then put new marks on your paper using your best guess again a little more or less than before, and repeat. The result: pretty soon you will hit it near enough. Mathematically what you have done is to create a convergent sequence of marks on your paper, which might be either a monotone sequence if you are very cautious, or requires the squeeze theorem if you are a little more aggressive in your adjustments.

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Here's a simple formula for figuring this out.

(A-(Bx2))/(C-1)

where:

A = Length of your board

B = Distance of First Hook From Edge of Board

C = Total Number of Hooks

Here is an Excel 2007 spreadsheet that will do the work for you. All you have to do is enter the values of A, B, & C.

Hope this helps!

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