Question

Find the coordinates of the point which divides the line segment joining the points $(5,-2)$ and $(9,6)$ in the ratio $3:1$.

Answer 1

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

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Let the points be $A(5,-2)$ and $B(9,6)$. Let a point $P(x,y)$ divides $AB$ in the ratio $3:1$.

Therefore, we have

$P(x,y)=(\frac{3\times 9+1\times 5}{3+1},\frac{3\times 6+1\times (-2)}{3+1})$

$P(x,y)=(8,4)$

Hence, the required point is $(8,4)$.