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.

\[ f(A) \leq \max (f(P), f(Q), f(R)) \]

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## Comments

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

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