Precalculus (6th Edition)

a. $13$ b. $(1,-\displaystyle \frac{7}{2})$
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. $P(-5,-6), Q(7, -1)$. $d(P, Q)=\sqrt{(7-(-5))^{2}+(-1-(-6))^{2}}$ $=\sqrt{12^{2}+5^{2}}=\sqrt{144+25}=\sqrt{169}=13$ b. $M=(\displaystyle \frac{-5+7}{2},\frac{-6+(-1)}{2})=(1,-\frac{7}{2})$