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

$$\mathrm{The}\mathrm{coordinates}\mathrm{of}\mathrm{A},\mathrm{B},\mathrm{C}\mathrm{are}$$ $$(6,3),(-3,5)\mathrm{and}(4,-2)\mathrm{respectively}$$ $$\mathrm{and}\mathrm{P}\mathrm{is}\mathrm{any}\mathrm{point}(\mathrm{x},\mathrm{y}).\mathrm{Find}\mathrm{ratio}$$ $$\mathrm{of}\mathrm{area}△\mathrm{PBC}\mathrm{\&}△\mathrm{ABC}.$$

Answered by EDWIN88 last updated on 09/May/21

$$\mathrm{area}△\mathrm{PBC}=\frac{1}{2}\mid \left|\begin{array}{c}\mathrm{x}\mathrm{y}1\\ -351\\ 4-21\end{array}\right|\mid =\frac{7}{2}\mid \mathrm{x}+\mathrm{y}-7\mid$$ $$\mathrm{area}△\mathrm{ABC}=\frac{1}{2}\mid \left|\begin{array}{c}631\\ -351\\ 4-21\end{array}\right|\mid =\frac{49}{2}$$ $$\frac{\mathrm{area}△\mathrm{PBC}}{\mathrm{area}△\mathrm{ABC}}=\frac{\mid \mathrm{x}+\mathrm{y}-7\mid }{7}.$$

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