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# Function

Consider a triangle $$PQR$$ in int the cartesian plane. Let $$A$$ be a point lying on triangle $$PQR$$ or inside the region enclosed by it . Prove that, for any function $$f(x,y)=ax+by+c$$ on the cartesian plane, the inequation below holds true.

$f(A) \leq \max (f(P), f(Q), f(R))$

Note by Pratik Roy
1 year, 9 months ago

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Use the fact that the distance of a point $$(x_0, y_0)$$ is $$\left|\dfrac{ax_0 + by_0 + c}{\sqrt{a^2 + b^2}}\right|$$.

- 1 year, 9 months ago