How many lines can be formed from 17 points

where no 3 points are collinear?

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

n(n + 1)
2

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:

17(17 - 1)
2

17(16)
2

272
2


The number of lines that can be formed from 17 points no 3 of which are collinear is 136


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What is the Answer?
The number of lines that can be formed from 17 points no 3 of which are collinear is 136
How does the Collinear Points that form Unique Lines Calculator work?
Free Collinear Points that form Unique Lines Calculator - Solves the word problem, how many lines can be formed from (n) points no 3 of which are collinear.
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What 1 formula is used for the Collinear Points that form Unique Lines Calculator?
The number of lines that can be formed from n points of which no 3 are collinear is n(n + 1)/2
What 4 concepts are covered in the Collinear Points that form Unique Lines Calculator?
collinear
points that lie on a straight line
collinear points that form unique lines
line
an infinitely long one-dimensional object with no width, depth, or curvature
point
an exact location in the space, and has no length, width, or thickness
Example calculations for the Collinear Points that form Unique Lines Calculator
Collinear Points that form Unique Lines Calculator Video

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