Question

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

Answer 1

Answer:

There is a small correction in the question.

The line would be 3x + 4y - 9 = 0

Let the line 3x + 2y - 9 = 0 divide the line segment joining ( 1,3 ) and ( 2,7 ) in the ratio of k:1.

=> X coordinate = $\dfrac{ 2k + 1 }{k+1}$

=> Y coordinate = $\dfrac{7k+3}{k+1}$

Substituting the values we get,

$\implies 3 ( \dfrac{ 2k+ 1}{k+1}) + 4 ( \dfrac{7k + 3 }{k+1}) = 9\\\\\\\implies \dfrac{6k+3}{k+1} + \dfrac{28k+12}{k+1} = 9\\\\\\\implies \dfrac{34k+15}{k+1} = 9\\\\\text{Cross multiplying we get,}\\\\\\\implies 34k + 15 = 9k + 9\\\\\implies 34k - 9k = 9 - 15\\\\\implies 25k = -6\\\\\implies k = \dfrac{-6}{25}$

Since k is negative, the line is divided externally

=> k:1 = 6/25 : 1 which is 6 : 25

Hence the ratio of division is 6 : 25 externally.