Question

In what ratio is the line joining the points $(-5,1)$ and $(2,3)$ divided by the y-axis? Also, find the point of intersection.

• A. $5:2$ internally, $(0,\frac{17}{7})$
• B. $5:2$ internally, $(0,\frac{12}{7})$
• C. $5:2$ internally, $(0,\frac{17}{5})$
• D. None of these

Answer 1

The correct option is A $5:2$ internally, $(0,\frac{17}{7})$

Equation of the line passing from points $A$ and $B$ is $L:7y-2x=17$.

Let line $L$ intersect the $y-axis$ at $P(x,y)$.

Since for $y-axis:-x=0$.

Putting $x=0$ in equation of line:

$y=\frac{17}{7}$. So, point $P(x,y)=(0,\frac{17}{7})$.

Now, $P$ lies on line $L$, so let's assume it divides line $AB$ in ratio $m:1$.

By section formula:

$0=\frac{2m-5}{m+1}=>m=\frac{5}{2}$.

Hence the required ratio is $(5:2)$.