# Half Way Points

Geometry Level 5

As shown, $$ABC$$ is a right angle triangle with $$\angle A = 90^\circ$$ and $$BC=100$$. $$D$$ is the midpoint of $$AB$$ and equation of $$CD$$ is $$y=3x+4$$; $$E$$ is the midpoint of $$AC$$ and equation of $$BE$$ is $$y=6-5x$$. Given that the area of triangle $$ABC$$ is $$\dfrac{p}{q}$$, where $$p$$ and $$q$$ are coprime positive integers, find $$p+q$$.

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