How many lines can be formed from 17 points where no 3 points are collinear?

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How many lines can be formed from 17 points

where no 3 points are collinear?

The formula for this is below for (n) points:

To get this formula, we list our 17 points are listed below:

P₁,P₂,P₃,P₄,P₅,P₆,P₇,P₈,P₉,P₁₀,P₁₁,P₁₂,P₁₃,P₁₄,P₁₅,P₁₆,P₁₇

List our unique pairings:

P₁ can be uniquely paired into the following 16 points:

(P₁,P₂),(P₁,P₃),(P₁,P₄),(P₁,P₅),(P₁,P₆),(P₁,P₇),(P₁,P₈),(P₁,P₉),(P₁,P₁₀),(P₁,P₁₁),(P₁,P₁₂),(P₁,P₁₃),(P₁,P₁₄),(P₁,P₁₅),(P₁,P₁₆),(P₁,P₁₇)

P₂ can be uniquely paired into the following 15 points:

(P₂,P₃),(P₂,P₄),(P₂,P₅),(P₂,P₆),(P₂,P₇),(P₂,P₈),(P₂,P₉),(P₂,P₁₀),(P₂,P₁₁),(P₂,P₁₂),(P₂,P₁₃),(P₂,P₁₄),(P₂,P₁₅),(P₂,P₁₆),(P₂,P₁₇)

P₃ can be uniquely paired into the following 14 points:

(P₃,P₄),(P₃,P₅),(P₃,P₆),(P₃,P₇),(P₃,P₈),(P₃,P₉),(P₃,P₁₀),(P₃,P₁₁),(P₃,P₁₂),(P₃,P₁₃),(P₃,P₁₄),(P₃,P₁₅),(P₃,P₁₆),(P₃,P₁₇)

P₄ can be uniquely paired into the following 13 points:

(P₄,P₅),(P₄,P₆),(P₄,P₇),(P₄,P₈),(P₄,P₉),(P₄,P₁₀),(P₄,P₁₁),(P₄,P₁₂),(P₄,P₁₃),(P₄,P₁₄),(P₄,P₁₅),(P₄,P₁₆),(P₄,P₁₇)

P₅ can be uniquely paired into the following 12 points:

(P₅,P₆),(P₅,P₇),(P₅,P₈),(P₅,P₉),(P₅,P₁₀),(P₅,P₁₁),(P₅,P₁₂),(P₅,P₁₃),(P₅,P₁₄),(P₅,P₁₅),(P₅,P₁₆),(P₅,P₁₇)

P₆ can be uniquely paired into the following 11 points:

(P₆,P₇),(P₆,P₈),(P₆,P₉),(P₆,P₁₀),(P₆,P₁₁),(P₆,P₁₂),(P₆,P₁₃),(P₆,P₁₄),(P₆,P₁₅),(P₆,P₁₆),(P₆,P₁₇)

P₇ can be uniquely paired into the following 10 points:

(P₇,P₈),(P₇,P₉),(P₇,P₁₀),(P₇,P₁₁),(P₇,P₁₂),(P₇,P₁₃),(P₇,P₁₄),(P₇,P₁₅),(P₇,P₁₆),(P₇,P₁₇)

P₈ can be uniquely paired into the following 9 points:

(P₈,P₉),(P₈,P₁₀),(P₈,P₁₁),(P₈,P₁₂),(P₈,P₁₃),(P₈,P₁₄),(P₈,P₁₅),(P₈,P₁₆),(P₈,P₁₇)

P₉ can be uniquely paired into the following 8 points:

(P₉,P₁₀),(P₉,P₁₁),(P₉,P₁₂),(P₉,P₁₃),(P₉,P₁₄),(P₉,P₁₅),(P₉,P₁₆),(P₉,P₁₇)

P₁₀ can be uniquely paired into the following 7 points:

(P₁₀,P₁₁),(P₁₀,P₁₂),(P₁₀,P₁₃),(P₁₀,P₁₄),(P₁₀,P₁₅),(P₁₀,P₁₆),(P₁₀,P₁₇)

P₁₁ can be uniquely paired into the following 6 points:

(P₁₁,P₁₂),(P₁₁,P₁₃),(P₁₁,P₁₄),(P₁₁,P₁₅),(P₁₁,P₁₆),(P₁₁,P₁₇)

P₁₂ can be uniquely paired into the following 5 points:

(P₁₂,P₁₃),(P₁₂,P₁₄),(P₁₂,P₁₅),(P₁₂,P₁₆),(P₁₂,P₁₇)

P₁₃ can be uniquely paired into the following 4 points:

(P₁₃,P₁₄),(P₁₃,P₁₅),(P₁₃,P₁₆),(P₁₃,P₁₇)

P₁₄ can be uniquely paired into the following 3 points:

(P₁₄,P₁₅),(P₁₄,P₁₆),(P₁₄,P₁₇)

P₁₅ can be uniquely paired into the following 2 points:

(P₁₅,P₁₆),(P₁₅,P₁₇)

P₁₆ can be uniquely paired into the following 1 points:

(P₁₆,P₁₇)

From this, we have the following number of point combos:

16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

Plugging our number of points into our shortcut formula, we get:

You have 2 free calculationss remaining

Collinear Points that form Unique Lines Calculator Video

Tags:

• collinear points that form unique lines
• collinear
• line
• point