Answer
See below.
Work Step by Step
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) $d=\sqrt{(3-(-2))^2+(-5-(-3))^2}=\sqrt{25+4}=\sqrt{29}.$
b)$M=(\frac{-2+3}{2},\frac{-3+(-5)}{2})=(\frac{1}{2},-4)$.
c) By using the slope formula, $m=\frac{y_2-y_1}{x_2-x_1}=\frac{-5-(-3)}{3-(-2)}=\frac{-2}{5}.$
