Question

What will be the value of $y$ if the point $\left(\begin{array}{c}\frac{23}{5},y\end{array}\right)$, divides the line segment joining the points $(5,7)$ and $(4,5)$ in the ratio $2:3$ internally?

• A. $\frac{51}{5}$
• B. $\frac{11}{5}$
• C. $\frac{21}{5}$
• D. $\frac{31}{5}$

Answer 1

The correct option is D $\frac{31}{5}$

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ 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 $(x_1,y_1)=(5,7)$ and $(x_2,y_2)=(4,5)$ and $m=2,n=3$ in the section formula,

we get the point $(\frac{2\left(4\right)+3\left(5\right)}{2+3},\frac{2\left(5\right)+3\left(7\right)}{2+3})$$=(\frac{23}{5},\frac{31}{5})$
Hence, $y=\frac{31}{5}$