## Precalculus (10th Edition)

a) $5.$ b)$(-1/2,1)$.
The distance formula from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. The midpoint $M$ of the line segment from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is: $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$. Hence: a) $d=\sqrt{(1-(-2))^2+(-1-3)^2}=\sqrt{9+16}=\sqrt{25}=5.$ b)$M=(\frac{1+(-2)}{2},\frac{-1+3}{2})=(-1/2,1)$.