# Determine the ratio in which the line 3x + 4y - 9 = 0 divides the line segment joining the points (1,3) and (2,7).

Let the line

$3x + 4y - 9 = 0$

divides the line segment joining the points (1,3) and (2,7) in the ratio K:1

Then the coordinate of the point =

$(\frac{2k + 1}{k +1}, \frac{7k + 3}{k + 1})$

Since this the intersection point, it does lie on the line      $3x + 4y - 9 = 0$

then put the coordinate point

$3 \times (\frac{2k+1}{k+1}) + 4 \times (\frac{7k + 3}{k+1}) - 9 = 0 \\ 3 \times (2k + 1) + 4 \times (7k + 3) - 9 (k + 1) = 0 \\ 6k + 3 + 25k + 12 -9k - 9 = 0 \\ 25k = - 6 \\ k = \frac{-6}{25}$

Since K is negative, the line      $3x + 4y - 9 = 0$ divides the line segment joining the point (1,3) and (2, 7) the ratio 6: 25

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