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O is the origin and P, Q are points on the line $3 x + 4 y + 15 = 0$ such that OP=OQ=9 then the area of $Δ O P Q$ is

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$6 \sqrt{2}$

$9 \sqrt{2}$

$12 \sqrt{2}$

$18 \sqrt{2}$

answer is D.

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Detailed Solution

$h = \frac{| 3 (0) + 4 (0) + 15 |}{\sqrt{9 + 16}} = 3$
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$\begin{array}{l} m Q == \sqrt{81 - 9} = 6 \sqrt{2} \\ △ P O Q = 2 \times \frac{1}{2} \times 6 \sqrt{2} \times 3 = 18 \sqrt{2} \end{array}$

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