Question

The ratio in which the line 3x+4y-7=0 divides the line joining the points (1,2),(2,3) is-

• A. 4:11 Internally
• B. 4:11 Externally
• C. 7:11 Internally
• D. 7:11 Externally

Answer 1

The correct option is A 4:11 Internally

Let the point $(x,y)$ divides $AB$ in the ratio $k:1$.

By section formula,

$x=\frac{2k+1}{k+1},y=\frac{3k+2}{k+1}$

Now, this point also lies on the given line so it would satisfy the equation $3x+4y-7=0$

$\therefore ,3\left(\frac{2k+1}{k+1}\right)+4\left(\frac{3k+2}{k+1}\right)-7=0$

$\Rightarrow 6k+3+12k+8-7k-7=0$

$\Rightarrow 11k+4=0$

$\therefore k=\frac{-4}{11}$

Hence the ratio is $4:11$ externally.