Answer
(a) $\sqrt {34}$
(b) $(\frac{3}{2},-\frac{3}{2})$
(c) $y=\frac{5}{3}x-4$
Work Step by Step
(a) Given $P(0,-4), Q(3,1)$, we can fine the distance $d(P, Q)=\sqrt {(0-3)^2+(-4-1)^2}=\sqrt {34}$
(b) the coordinates of the midpoint of the segment PQ can be found as $(\frac{0+3}{2},\frac{-4+1}{2})$ or $(\frac{3}{2},-\frac{3}{2})$
(c) Assume the equation passing the two points as $y=mx+b$, we have $m=\frac{-4-1}{0-3}=\frac{5}{3}$ and $b=-4$, thus the equation is $y=\frac{5}{3}x-4$
