Question

The point which divides the line segment joining the points (3, 5) and (8, 10) internally in the ratio 2:3 is:

• A. 3, 5
• B. 5, 3
• C. 5, 7
• D. 7, 5

Answer 1

The correct option is C 5, 7

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 $(x_1,y_1)=(3,5)$ and $(x_2,y_2)=(8,10)$ and $m=2,n=3$ in the section formula, we get
the point $(\frac{2\left(8\right)+3\left(3\right)}{2+3},\frac{2\left(10\right)+3\left(5\right)}{2+3})=(5,7)$