<-- Enter number of points
  

How many lines can be formed from 10 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 10 points are listed below:

P1,P2,P3,P4,P5,P6,P7,P8,P9,P10

List our unique pairings:

P1 can be uniquely paired into the following 9 points:

(P1,P2),(P1,P3),(P1,P4),(P1,P5),(P1,P6),(P1,P7),(P1,P8),(P1,P9),(P1,P10)

P2 can be uniquely paired into the following 8 points:

(P2,P3),(P2,P4),(P2,P5),(P2,P6),(P2,P7),(P2,P8),(P2,P9),(P2,P10)

P3 can be uniquely paired into the following 7 points:

(P3,P4),(P3,P5),(P3,P6),(P3,P7),(P3,P8),(P3,P9),(P3,P10)

P4 can be uniquely paired into the following 6 points:

(P4,P5),(P4,P6),(P4,P7),(P4,P8),(P4,P9),(P4,P10)

P5 can be uniquely paired into the following 5 points:

(P5,P6),(P5,P7),(P5,P8),(P5,P9),(P5,P10)

P6 can be uniquely paired into the following 4 points:

(P6,P7),(P6,P8),(P6,P9),(P6,P10)

P7 can be uniquely paired into the following 3 points:

(P7,P8),(P7,P9),(P7,P10)

P8 can be uniquely paired into the following 2 points:

(P8,P9),(P8,P10)

P9 can be uniquely paired into the following 1 points:

(P9,P10)

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

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

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

10(10 - 1)
2

10(9)
2

90
2

The number of lines that can be formed from 10 points no 3 of which are collinear is 45


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What is the Answer?
The number of lines that can be formed from 10 points no 3 of which are collinear is 45
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.
This calculator has 1 input.

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

For more math formulas, check out our Formula Dossier

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
  1. how many lines can be formed from 17 collinear points
  2. how many lines can be formed from 10 collinear points

Collinear Points that form Unique Lines Calculator Video


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