Question

Find coordinates of point which divides the line segment internally, joining the points $(5,7)$ and $(9,12)$ in ratio $2:4$.

• A. $\frac{26}{3},\frac{19}{3}$
• B. $\left(\begin{array}{c}\frac{19}{3},\frac{26}{3}\end{array}\right)$
• C. $19,26$
• D. None

Answer 1

Answer: (B)

$\left(\begin{array}{c}\frac{19}{3},\frac{26}{3}\end{array}\right)$

We know that 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, we have

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

Hence $m=2,n=4,x_1=5,x_2=9,y_1=7,y_2=12$

$\therefore$ $x=\frac{(5\times 4)+(9\times 2)}{6}$

and

$y=\frac{(7\times 4)+(12\times 2)}{6}$

$x=\frac{20+18}{6}$ and $y=\frac{28+24}{6}$

$x=\frac{38}{6}=\frac{19}{3}$ and $y=\frac{52}{6}=\frac{26}{3}$

$(x,y)\Rightarrow \left(\begin{array}{c}\frac{19}{3},\frac{26}{3}\end{array}\right)$