#### Answer

a. $3\sqrt{41}$
b. $(0,\displaystyle \frac{5}{2})$

#### 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.
$P(-6,-5), Q(6,10)$.
$d(P, Q)=\sqrt{(6-(-6))^{2}+(10-(-5))^{2}}$
$=\sqrt{(12)^{2}+(15)^{2}}=\sqrt{144+225}=\sqrt{369}$
$=\sqrt{9\times 41}=3\sqrt{41}$
b.
$M=(\displaystyle \frac{-6+6}{2},\frac{-5+10}{2})=(0,\frac{5}{2})$