Question

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

Answer 1

Formula: 1 Mark
Application: 1 Mark
Answer: 1 Mark


Suppose the line 3x + y -9 = 0 divides the line segment joining A(1, 3) and B(2, 7) in the ratio k:1 at point C.

Then, the coordinates of C are

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

But, C lies on 3x + y -9 = 0. Therefore,

$3\left(\frac{2k+1}{k+1}\right)+1\left(\frac{7x+3}{k+1}\right)-9=0$

$\Rightarrow 6k+3+7k+3-9k-9=0$

$\Rightarrow k=\frac{3}{4}$

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