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 |
What is the Answer?
How does the Collinear Points that form Unique Lines Calculator work?
This calculator has 1 input.
What 1 formula is used for the Collinear Points that form Unique Lines Calculator?
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
