Question

Find coordinates of point which divides the line segment internally, joining the points $(9,18)$ and $(1,2)$ in ratio $3:6$.

• A. $\frac{36}{3},\frac{20}{3}$
• B. $\frac{20}{3},\frac{38}{3}$
• C. $20,38$
• D. None

Answer 1

Answer: (D)

None

As we know if a point $P(x,y)$ divides the line segment $AB$ joining the points $A(x_1,y_1)\&B(x_2,y_2)$ in the ratio $m:n$ then, by the section formula,

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

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

$m=3,n=6,x_1=9,x_2=1,y_1=18,y_2=2$

By section formula for internal division,
$x=\frac{9\times 6+3\times 1}{9}$ and $y=\frac{18\times 6+2\times 3}{9}$

$x=\frac{54+3}{9}$ and $y=\frac{108+6}{9}$

$x=\frac{57}{9}$ and $y=\frac{114}{9}$

$x=\frac{19}{3}$ and $y=\frac{38}{3}$