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

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(A) The total number of intersection points for $37$ straight lines,if no three were concurrent and no two were parallel,would be $^{37}C_2$.Since $13

Vedclass · Accepted Answer

$535$

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

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