Question

The point $(1,3)$ divide the line segment joining the points $(3,6)$ and $(-5,-6)$ internally in the ratio

• A. $1:3$
• B. $1:2$
• C. $1:4$
• D. $2:3$

Answer 1

The correct option is A $1:3$

Let the point $R(x,y)=(1,3)$ divides the line segment $PQ$ joining the points $P(x_1,y_1)=(3,6)$

and $Q(x_2,y_2)\equiv (-5,-6)$ in the ratio $m:n$

Then $x=\frac{n{x}_1+m{x}_2}{m+n}$
$1=\frac{3n+(-5)m}{m+n}$

$6m=2n$

$m:n=1:3$

Similarly, if we take $y=\frac{n{y}_1+m{y}_2}{m+n}$

$3m=n$

$m:n=1:3$