#### Answer

a. $\sqrt{202}$
b. $(-\displaystyle \frac{5}{2},-\frac{1}{2})$

#### 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.
$P(-8,4), Q(3,-5)$.
$d(P, Q)=\sqrt{(3-(-8))^{2}+(-5-4)^{2}}$
$=\sqrt{(11)^{2}+(-9)^{2}}=\sqrt{121+81}=\sqrt{202}$
b.
$M=(\displaystyle \frac{-8+3}{2},\frac{4+(-5)}{2})=(-\frac{5}{2},-\frac{1}{2})$