The-coordinates-of-A-B-C-are-6-3-3-5-and-4-2-respectively-and-P-is-any-point-x-y-Find-ratio-of-area-PBC-amp-ABC-

Question Number 140555 by liberty last updated on 09/May/21

The coordinates of A, B, C are

(6, 3), (- 3, 5) and (4, - 2) respectively

and P is any point (x, y) . Find ratio

of area △ PBC & △ ABC .

Answered by EDWIN88 last updated on 09/May/21

area △ PBC = \frac{1}{2} ∣ | \begin{matrix} x y 1 \\ - 3 5 1 \\ 4 - 2 1 \end{matrix} | ∣ = \frac{7}{2} ∣ x + y - 7 ∣

area △ ABC = \frac{1}{2} ∣ | \begin{matrix} 6 3 1 \\ - 3 5 1 \\ 4 - 2 1 \end{matrix} | ∣= \frac{49}{2}

\frac{area △ PBC}{area △ ABC} = \frac{∣ x + y - 7 ∣}{7} .

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