Question

Find the ratio in which the point P(1, 2) divides the line joining the points A(-2, 1) and B(7, 4).

• A. 1:2
• B. 2:3
• C. 3:4
• D. 1:3

Answer 1

The correct option is A 1:2

By section formula, we have, if (x,y) divides the line segments joining $(x_1,y_1)$ and $(x_2,y_2)$ internally in the ratio m:n then,

$x$ = $\frac{m{x}_2+n{x}_1}{m+n}$ and $y$ = $\frac{m{y}_2+n{y}_1}{m+n}$
Here,
$(x_1,y_1)=(-2,1)$,
$(x_2,y_2)=(7,4)$,
$(x,y)=(1,2)$

$\Rightarrow 1=\frac{7m-2n}{m+n}\Rightarrow 7m-2n=m+n\Rightarrow 6m=3n\Rightarrow \frac{m}{n}=\frac{3}{6}=\frac{1}{2}$

$\therefore$ The ratio in which 'P' divides AB is 1 : 2