Freeflows
Mean Line Slope
Let $ w_1, w_2, \dots, w_n $ be complex numbers. A line $ L $ in the complex plane is called a mean line for the points $ w_1, w_2, \dots, w_n $ if $ L $ contains points (complex numbers) $ z_1, z_2, \dots, z_n $ such that \[\sum_{k = 1}^n (z_k - w_k) = 0.\]For the numbers $ w_1 = 32 + 170i $, $ w_2 = -7 + 64i $, $ w_3 = -9 +200i $, $ w_4 = 1 + 27i $, and $ w_5 = -14 + 43i $, there is a unique mean line with $ y $-intercept $ 3 $. Find the slope of this mean line.
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- 9
- $\frac{a}{b}$
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- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$