Find The Length Of Every Line Segment That Can Be Drawn By Connecting Dots On A 3 Dot-by-3 Dot Grid?
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Possible lines on a grid where the dots are 1 unit apart are
1) horizontal or vertical to an adjacent dot, length = 1
2) diagonal (over one and up one), length = sqrt[12+12] = sqrt[2]
3) horizontal or vertical through an adjacent dot to the one beyond, length = 2
4) over 2 dots and up 1, or over 1 dot and up 2, length = sqrt[12+22] = sqrt[5]
5) over 2 dots and up 2 dots, length = sqrt[22+22] = 2*sqrt[2]
1) horizontal or vertical to an adjacent dot, length = 1
2) diagonal (over one and up one), length = sqrt[12+12] = sqrt[2]
3) horizontal or vertical through an adjacent dot to the one beyond, length = 2
4) over 2 dots and up 1, or over 1 dot and up 2, length = sqrt[12+22] = sqrt[5]
5) over 2 dots and up 2 dots, length = sqrt[22+22] = 2*sqrt[2]
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