What is the greatest possible number of points of intersection for eight distinct lines in a plane?

Guest Nov 7, 2019

#1**+3 **

Draw two lines

there is one point of intersection

Draw 3 lines, there is 3 points of intersections

Draw 4 lines, there is 6 points of intersections

Draw 5 lines, there is 10 points of intersection

List:

Number of lines | Number of Intersections | Rule or Pattern |

2 | 1 | +1 |

3 | 3 | +2 |

4 | 6 | +3 |

5 | 10 | +4 |

6 | 15 | +5 |

7 | 21 | +6 |

8 | 28 | +7 |

Answer | should be | 28 |

Don't trust me, I might've gotten it wrong.

CalculatorUser Nov 7, 2019

#2**+2 **

**What is the greatest possible number of points of intersection for eight distinct lines in a plane?**

Let \(\mathbf{n}\) is the number of lines.

The greatest possible number of points of intersection for \(\mathbf{n}\) distinct lines in a plane is : \(\dbinom{n}{2}\)

Here \(n = 8\):

\(\begin{array}{|rcll|} \hline && \dbinom{n}{2} \\\\ &=& \dbinom{8}{2} \\\\ &=& \dfrac{8}{2}\cdot \dfrac{7}{1} \\\\ &=& \mathbf{28} \\ \hline \end{array} \)

heureka Nov 8, 2019