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

Answers (1)

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 = 

                                                        $$(frac2k + 1k +1, frac7k + 3k + 1) $$

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

then put the coordinate point

                                                   $$ 3 	imes (frac2k+1k+1) + 4 	imes (frac7k + 3k+1) - 9 = 0 $$\$$ $$ 3 	imes (2k + 1) + 4 	imes (7k + 3) - 9 (k + 1) = 0 $$\$$ $$6k + 3 + 25k + 12 -9k - 9 = 0 $$\$$ $$ 25k = - 6 $$\$$ $$ k = frac-625 $$

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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