Mock AIME 1 2006-2007 Problems/Problem 4

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4. $\triangle ABC$ has all of it's verticies on the parabola $y=x^{2}$. The slopes of $AB$ and $BC$ are $10$ and $-9$, respectively. If the x-coordinate of the triangle's centroid is $1$, find the area of $\triangle ABC$.

Mock AIME 1 2006-2007