Question

The co-ordinates of the point Q$(x,y)$ which divides the line segment joining A$(-2,1)$ and B$(1,4)$ in the ratio $2:1$ are

• A. $(2,1)$
• B. $(-3,2)$
• C. $(0,3)$
• D. $(-4,2)$

Answer 1

Answer: (C)

$(0,3)$

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ internally in the ratio $m:n$, then $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Substituting $(x_1,y_1)=(-2,1)$ and $(x_2,y_2)=(1,4)$ and $m=2,n=1$ in the section formula, we get the
point as

$Q=(\frac{2\left(1\right)+1(-2)}{2+1},\frac{2\left(4\right)+1\left(1\right)}{2+1})=(\frac{2+(-2)}{3},\frac{8+1}{3})=(0,3)$