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$$\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}$$ = $$13$$
$$(-5-7)^{2}+(k-2)^{2}$$ = $$169$$
$$144+(k-2)^{2}$$ = $$169$$
$$(k-2)^{2}$$ = $$169-144$$
$$k-2 = 5$$
$$ k = 7$$
So the answer is option B.
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