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If A(6,3),B(-3,5), C(4,-2) and P(a,b) then the ratio of the areas of the triangles PBC,ABC is

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$|a + b + 2| : 7$

$|a - b| : 7$

$|a + b - 2| : 7$

$|a + b| : 7$

answer is D.

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Detailed Solution

$P (a, b), A = (6, 3), B (- 3, 5), C = (4, - 2)$

$Area of triangle = \frac{1}{2} |\begin{array}{ll} x_{1} - x_{2} y_{1} - y_{2} \\ x_{1} - x_{3} y_{1} - y_{3} \end{array}|$

$Area of △ P B C : Area of △ A B C$

$\frac{1}{2} | 7 a + 7 b - 14 | : \frac{1}{2} 49 \Rightarrow | a + b - 2 | : 7$

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