#### Answer

a. $\sqrt{34}$
b. $(\displaystyle \frac{11}{2},\frac{7}{2})$

#### Work Step by Step

Let $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$.
$d(P, Q)=\sqrt{(x_{2}-x_{\mathrm{I}})^{2}+(y_{2}-y_{1})^{2}}$
$M=(\displaystyle \frac{x_{\mathrm{I}}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
-----------------------
a.
$P(8,2), Q(3,5)$.
$d(P, Q)=\sqrt{(3-8)^{2}+(5-2)^{2}}$
$=\sqrt{(-5)^{2}+3^{2}}=\sqrt{25+9}=\sqrt{34}$
b.
$M=(\displaystyle \frac{8+3}{2},\frac{2+5}{2})=(\frac{11}{2},\frac{7}{2})$