Question

The co-ordinates of the point A which divide the line segment $GH$ joining the points $G(-4,12)$ and $H(11,-3)$ internally in the ratio $m:n=2:3$ are

• A. $A(x,y)=(1,3)$
• B. $A(x,y)=(2,3)$
• C. $A(x,y)=(2,6)$
• D. $A(x,y)=(1,6)$

Answer 1

Answer: (C)

$A(x,y)=(2,6)$

Given that the point $A(x,y)$ divides the line segment $GH$ joining the points

$G(x_1,y_1)=(-4,12)$ & $H(x_2,y_2)=(11,-3)$ in the ratio $m:n=2:3$.

We know that if a point $A(x,y)$ divides the line segment $GH$ joining the points

$G(x_1,y_1)$ & $H(x_2,y_2)$ in the ratio $m:n$ then, by the section formula,

$x=\frac{m{x}_2+n{x}_1}{m+n}$ & $y=\frac{m{y}_2+n{y}_1}{m+n}$

$\therefore$ The co-ordinates of A are

$x=\frac{2\times \left(11\right)+3\times (-4)}{2+3}=\frac{10}{5}=2$

And $y=\frac{2\times (-3)+3\times 12}{2+3}=\frac{30}{5}=6$

$\therefore A(x,y)=(2,6)$