Parthi and Alisha found a treasure that is exactly on the straight line joining their locations. Parthi's location is at point $\displaystyle (- 6, - 5)$ and Alisha's location is at point $\displaystyle (10, 11)$. The distance from the treasure to Parthi's location is three times that of the distance to Alisha's location. Find the coordinates of the location of the treasure.

Let the points P, A and T represent the location of Parthi, Alisha and Treasure respectively. Let the cordinates of T be \(\displaystyle (x, y)\) \[\begin{array}{ccccc} \mathbf{P} & 3 & \boldsymbol{\top} & 1 & \boldsymbol{A} \\ (-6,-5) & (x, y) & (10, & 11) \end{array} \] \[\begin{aligned} & \mathrm{PT}=3 \mathrm{AT} \\ & \Rightarrow \frac{\mathrm{PT}}{\mathrm{AT}}=\frac{3}{1} \end{aligned} \] Coordinates of T are \(\displaystyle \left(\frac{10 \times 3-6}{3+1}, \frac{11 \times 3-5}{3+1}\right)\) \[=(6,7) \]