Parthi and Alisha found a treasure that is exactly on the straight line joining their locations. Parthi's location is at point (- 6, - 5) and…

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 \(\displaystyle \left(\frac{10 \times 3-6}{3+1}, \frac{11 \times 3-5}{3+1}\right)\) \[=(6,7) \]