#### Answer

a. $10$
b. $(-1,-1)$

#### 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.
$P(-4,3), Q(2, -5)$.
$d(P, Q)=\sqrt{(2-(-4))^{2}+(-5-3)^{2}}$
$=\sqrt{6^{2}+8^{2}}=\sqrt{36+64}=\sqrt{100}=10$
b.
$M=(\displaystyle \frac{-4+2}{2},\frac{3+(-5)}{2})=(-1,-1)$