Answer
(a) $\sqrt (34)$
(b) $(\frac{11}{2}+\frac{7}{2})$
Work Step by Step
Part (a):
Finding the distance between P and Q,
$d(P,Q)=\sqrt ((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})$
$d(P,Q)=\sqrt ((8-3)^{2}+(2-5)^{2})$
$d(P,Q)=\sqrt ((5)^{2}+(-3)^{2})$
$d(P,Q)=\sqrt (25+9)$
$d(P,Q)=\sqrt (34)$
Part (b):
The midpoint formula is $(\frac{x_{1}+x_{2}}{2}+\frac{y_{1}+y_{2}}{2})$
Substituting the values, the formula becomes:
$(\frac{8+3}{2}+\frac{2+5}{2})=(\frac{11}{2}+\frac{7}{2})$
Therefore, the coordinates of the midpoint are: $(\frac{11}{2}+\frac{7}{2})$
