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Suppose you have 10 points in the plane with no three collinear.

 

(a) How many different line segments are formed by joining pairs of of these points?

(b) How many different triangles are formed by these line segments?

(c) If A is one of the 10 points, how many of the triangles formed by the line segments have A as a vertex?

 Feb 26, 2020
 #1
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(a) How many different line segments are formed by joining pairs of of these points?

 

I don't know the answers to (b)  or (c)   but for this one we have

 

n ( n -1)        10  *  9

________  =  _______  =      45

    2                     2

 

See here  for a  simple  derivation of the  formula  :

 

https://www.basic-mathematics.com/number-of-segments.html

 

 

 

cool cool cool

 Feb 26, 2020

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