#### Answer

a. $2\sqrt{17}$
b. $(5,2)$

#### 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.
$P(6,-2), Q(4,6)$.
$d(P, Q)=\sqrt{(4-6)^{2}+(6-(-2))^{2}}$
$=\sqrt{(-2)^{2}+(8)^{2}}=\sqrt{4+64}=\sqrt{68}$
$=\sqrt{4\times 17}=2\sqrt{17}$
b.
$M=(\displaystyle \frac{6+4}{2},\frac{-2+6}{2})=(5,2)$