The coordinates of \( A, B, C \) are \( (7,4),(-2,6) \) and \( (5,-1) \), respectively and \( P ...

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The coordinates of \( A, B, C \) are \( (7,4),(-2,6) \) and \( (5,-1) \), respectively and \( P \) is any point \( (x, y) \). Show that the ratio of the areas of \( \triangle P B C \) and \( \triangle A B C \) is \( \left|\frac{x+y-4}{7}\right| \).
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