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$\frac{-12 + x_2}{2} = -20$
$\frac{13 + y_2}{2} = 14$
$-12 + x_2 = -40 \Rightarrow x_2 = -28$
$13 + y_2 = 28 \Rightarrow y_2 = 15$
$(x_2, y_2) = \boxed{(-28, 15)}$