1.

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

Answer»

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

Since this the INTERSECTION point, it also lies on the line 3x + 4y - 9 = 0.Thus

3(\frac{2k+1}{k+1}) + 4(\frac{7k+3}{k+1}) - 9 = 0\\ \\3(2k+1)+4(7k+3)-9(k+1)=0\\ \\6k+3+28k+12-9k-9=0\\ \\25k+6=0\\ \\25k=-6\\ \\k=- \frac{6}{25}

Since k is negative, the line 3x + 4y - 9 = 0 divides the line segment joining the points (1,3) and (2,7) externally in the ratio \boxed{6:25}


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