We do this by subtracting the components of $\vec{A}$ from the components of $\vec{B}$.
\[
\begin{align*}
\vec{G} &= -\vec{A} + \vec{B} \\
&= (-23.0, -59.0) + (90.0, -150.0) \\
&= (90.0 - 23.0, -150.0 - 59.0) \\
&= (67.0, -209.0)
\end{align*}
\]
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