Question

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

Answer 1

Step-by-step explanation:

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})(

k+1

2k+1

,

k+1

7k+3

) .

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

\begin{gathered}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}\end{gathered}

3(

k+1

2k+1

)+4(

k+1

7k+3

)−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=−

25

6

Answer 2

Step-by-step explanation:

$= \frac{25}{6}$

$hope \: its \: help \: you$