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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 Alisha's location is at point $(10, 11)$. 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.
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Let the points P, A and T represent the location of Parthi, Alisha and Treasure respectively.
Let the coordinates of T be $(x, y)$
P $(-6,-5)$ T $(x, y)$ A $(10, 11)$
$PT = 3 AT$ (1 Mark)
$\frac{PT}{AT} = \frac{3}{1}$ (1/2 Mark)
Coordinates of T are $(\frac{10\times3-6}{3+1}, \frac{11\times3-5}{3+1})$ (1 Mark)
$= (6,7)$ (1/2 Mark)
Let the coordinates of T be $(x, y)$
P $(-6,-5)$ T $(x, y)$ A $(10, 11)$
$PT = 3 AT$ (1 Mark)
$\frac{PT}{AT} = \frac{3}{1}$ (1/2 Mark)
Coordinates of T are $(\frac{10\times3-6}{3+1}, \frac{11\times3-5}{3+1})$ (1 Mark)
$= (6,7)$ (1/2 Mark)