Question

19.The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio​

Answer 1

Answer:

for finding the ratio, we must use section formula,

$M(x,y)=(\frac{mx2+nx1}{m+n} ,\frac{my2+ny1}{m+n} )$

here, the required ratio is m:n

so,  $(\frac{m2+n}{m+n} ,\frac{m7+n2}{m+n} )$

now putting the values in  3x + y – 9 = 0

$3(\frac{m2+n}{m+n}) + (\frac{m7+n2}{m+n} ) - 9 = 0$

$(\frac{6m+3n+7m+2n}{m+n})-9 = 0$

$\frac{13m+5n}{m+n}= 9$

$13m+5n=9m+9n$

$4m = 4n$

$m/n = 4/4$

$thus, m:n = 1:1$

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