Question

Find the ratio in which the $y$-axis divides the line segment joining the points $A(3,4)$ and $B(-2,1)$. Also, find the point of intersection.

• A. $3:2,(0,\frac{11}{5})$
• B. $1:2,(0,\frac{13}{5})$
• C. $1:2,(0,\frac{3}{5})$
• D. $3:4,(0,\frac{13}{5})$

Answer 1

Answer: (A)

$3:2,(0,\frac{11}{5})$

Let the ratio be k : 1. Then by which the section formula, the coordinates of the point which divides AB in the ratio k : 1 are $(\frac{-2k+3}{k+1},\frac{k+4}{k+1})$
This point lies on the y-axis, and on the y-axis, the abscissa is 0.
$\therefore \frac{-2k+3}{k+1}=0\Rightarrow -2k+3=0\Rightarrow k=3/2$
Hence, the ratio is 3 : 2.
Substituting this value of k, we get the point of intersection as (0, 11/5).