A point on a line segment

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$\text{Find the point }P \text{ on the line segment joining the points }A\left(\frac{1}{2},\frac{-1}{2}\right)\text{ and }B\left(\frac{-2}{5},-1\right)\text{ , such that }AP:PB =9:4$.

**Answer**

$\text{For the points }A \left(x_1,y_1\right) \text{ and }B\left(x_2,y_2\right)\text{ , if the point }P \text{ is such that }AP:PB=n:k \text{, then the point }P \text{ is given by:}$

$\left(\frac{(k)(x_1)+(n)(x_2)}{n + k},\frac{(k)(y_1)+(n)(y_2)}{n+k}\right)$$=\left(\frac{\frac{-8}{5}}{13},\frac{-11}{13}\right)=\left(\frac{-8}{65},\frac{-11}{13}\right)$