# Bisecting a Parallelogram

Geometry Level 4

Let $$A = (0,0)$$, $$B = (2,4)$$, $$C = (17,4)$$ and $$D = (15,0)$$. Then $$ABCD$$ is a parallelogram. A line through the point $$(0,-1)$$ divides the parallelogram into two regions of equal area. The slope of this line can be written as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are positive coprime integers. Find $$a+b$$.

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