Question

Ratio in which line $2x+3y-5=0$ divides the line segment joining the points A(8 , -9) and B(2 , 1) is .

• A. 8 : 1
• B. 7 : 1
• C. 8 : 3

Answer 1

The correct option is A 8 : 1

Let the ratio be k : 1.
Let P (x, y) divide A(8,-9) and B(2,1) in the ratio k : 1.
By section formula P (x , y) =$(\frac{2k+8}{k+1},\frac{k-9}{k+1})$
P$(\frac{2k+8}{k+1},\frac{k-9}{k+1})$ also lies on the line $2x+3y-5=0$
$\therefore$ $\frac{2(2k+8)}{k+1}+\frac{3(k-9)}{k+1}-5=0$
$\frac{4k+16}{k+1}+\frac{3k-27}{k+1}-5=0$
$4k+16+3k-27-5k-5=0$
$\Rightarrow 2k=16$
$\Rightarrow k=8$
Ratio in which the line $2x+3y-5=0$ divides the line segment joining the points A(8 , -9) and B(2 , 1) is 8 : 1.