Answer
(a) $\sqrt (202)$
(b) $(-\frac{5}{2},-\frac{1}{2})$
Work Step by Step
Let $P=(x_{1},y_{1})=(-8,4)$ and $Q=(x_{2},y_{2})=(3,-5)$
Part (a):
Finding the distance between P and Q,
$d(P,Q)=\sqrt ((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})$
$d(P,Q)=\sqrt ((3-(-8))^{2}+(-5-4)^{2})$
$d(P,Q)=\sqrt ((3+8)^{2}+(-9)^{2})$
$d(P,Q)=\sqrt ((11)^{2}+(-9)^{2})$
$d(P,Q)=\sqrt (121+81)$
$d(P,Q)=\sqrt (202)$
Part (b):
The midpoint formula is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
Substituting the values, the formula becomes:
$(\frac{-8+3}{2},\frac{4-5}{2})=(\frac{-5}{2},\frac{-1}{2})$
Therefore, the coordinates of the midpoint are: $(-\frac{5}{2},-\frac{1}{2})$
