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

 Nov 7, 2019
 #1
avatar+2557 
+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 linesNumber of IntersectionsRule or Pattern
21+1
33+2
46+3
510+4
615+5
721+6
828+7
Answershould be28

 

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

 Nov 7, 2019
edited by CalculatorUser  Nov 7, 2019
edited by CalculatorUser  Nov 8, 2019
 #2
avatar+23866 
+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 \(n = 8\):

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

 

laugh

 Nov 8, 2019
 #3
avatar+2557 
+1

wow so much easier

CalculatorUser  Nov 8, 2019

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