Answer
a. $13$
b. $(1,-\displaystyle \frac{7}{2})$
Work Step by Step
Let $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$.
$d(P, Q)=\sqrt{(x_{2}-x_{\mathrm{I}})^{2}+(y_{2}-y_{1})^{2}}$
$M=(\displaystyle \frac{x_{\mathrm{I}}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
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a.
$P(-5,-6), Q(7, -1)$.
$d(P, Q)=\sqrt{(7-(-5))^{2}+(-1-(-6))^{2}}$
$=\sqrt{12^{2}+5^{2}}=\sqrt{144+25}=\sqrt{169}=13$
b.
$M=(\displaystyle \frac{-5+7}{2},\frac{-6+(-1)}{2})=(1,-\frac{7}{2})$
