What is the greatest possible number of points of intersection for eight distinct lines in a plane?
+2862 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.
+26367 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 \(n = 8\):
\(\begin{array}{|rcll|} \hline && \dbinom{n}{2} \\\\ &=& \dbinom{8}{2} \\\\ &=& \dfrac{8}{2}\cdot \dfrac{7}{1} \\\\ &=& \mathbf{28} \\ \hline \end{array} \)
