In a plane,there are 37 straight lines,of whi | vedclass

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Question

(A) The total number of intersection points for $37$ lines,if no three were concurrent and no two were parallel,would be $^{37}C_2 = \frac{37 	imes 3

Vedclass · Accepted Answer

$535$

Vedclass · Answer

(A) The total number of intersection points for $37$ lines,if no three were concurrent and no two were parallel,would be $^{37}C_2 = \frac{37 	imes 36}{2} = 666$.However,$13$ lines pass through point $A$. These lines should have produced $^{13}C_2 = \frac{13 	imes 12}{2} = 78$ intersection points,but they only produce $1$ point. Thus,we must subtract $78$ and add $1$.Similarly,$11$ lines pass through point $B$. These lines should have produced $^{11}C_2 = \frac{11 	imes 10}{2} = 55$ intersection points,but they only produce $1$ point. Thus,we must subtract $55$ and add $1$.The total number of intersection points is $666 - 78 + 1 - 55 + 1 = 535$.

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