CEMC Cayley, 2006

Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

The line $y = -\frac{3}{4}x + 9$ crosses the $x$ -axis at $P$ and the $y$ -axis at $Q$ . Point $T(r,s)$ is on line segment $PQ$ . If the area of $\triangle POQ$ is three times the area of $\triangle TOP$ , then the value of $r + s$ is

(A) $7$ (B) $10$ (C) $11$ (D) $14$ (E) $18$

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