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# help

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

Nov 7, 2019

### 3+0 Answers

#1
+2847
+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.

Nov 7, 2019
edited by CalculatorUser  Nov 7, 2019
edited by CalculatorUser  Nov 8, 2019
#2
+24378
+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 $$n = 8$$:

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

Nov 8, 2019
#3
+2847
+1

wow so much easier

CalculatorUser  Nov 8, 2019