Let \(\tau_{A, B}\) represent a linear translation in the \(xy\)-plane from point \(A\) to point \(B\).

Given the points

- \(A=(21,42)\)
- \(B=(32,43)\)
- \(C=(-12,6)\)
- \(D=(-112,206),\)

if \(\tau_{A, B}\tau_{B,C}\tau_{C,D}\tau_{D,A}(2,8)=(a,b)\), what is \(a+b?\)

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