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MATH / Let w₁,w₂,…,w_(n) be complex numbers. A line L in the complex plane is called a mean line for the points w₁,w₂,…,w_(n) if L contains points (complex numbers) z₁,z₂,…,z_(n) such tha…

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Let w1,w2,…,wnw_1, w_2, \dots, w_n be complex numbers. A line LL in the complex plane is called a mean line for the points w1,w2,…,wnw_1, w_2, \dots, w_n if LL contains points (complex numbers) z1,z2,…,znz_1, z_2, \dots, z_n such that ∑k=1n(zk−wk)=0.\sum_{k = 1}^n (z_k - w_k) = 0.For the numbers w1=32+170iw_1 = 32 + 170i, w2=−7+64iw_2 = -7 + 64i, w3=−9+200iw_3 = -9 +200i, w4=1+27iw_4 = 1 + 27i, and w5=−14+43iw_5 = -14 + 43i, there is a unique mean line with yy-intercept 33. Find the slope of this mean line.
Plain-text mathematical notation (without MathML)
Let w₁,w₂,…,w_(n) be complex numbers. A line L in the complex plane is called a mean line for the points w₁,w₂,…,w_(n) if L contains points (complex numbers) z₁,z₂,…,z_(n) such that
∑_(k=1)^(n)(z_(k)−w_(k))=0.For the numbers w₁=32+170i, w₂=−7+64i, w₃=−9+200i, w₄=1+27i, and w₅=−14+43i, there is a unique mean line with y-intercept 3. Find the slope of this mean line.
Original LaTeX notation
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.

level

Level 5

type

Intermediate Algebra

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task_id
743c2de2-0f95-54b0-82e1-65cc60631d70
task_key
intermediate~5falgebra--test--743c2de2-0f95-54b0-82e1-65cc60631d70
task_revision_id
1
config / split
intermediate_algebra / test

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