let's first off, convert the mixed fractions to improper, and then get the midpoint.
[tex]\bf \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}}~\hfill \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}}
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~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
J(\stackrel{x_1}{\frac{5}{2}}~,~\stackrel{y_1}{-\frac{1}{4}})\qquad
K(\stackrel{x_2}{\frac{13}{4}}~,~\stackrel{y_2}{-1})
\qquad
\left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right)[/tex]
[tex]\bf \left( \cfrac{~~\frac{13}{4}+\frac{5}{2}~~}{2}~~,~~\cfrac{~~-1-\frac{1}{4}~~}{2} \right)\implies \left( \cfrac{~~\frac{13+10}{4}~~}{2}~~,~~\cfrac{~~\frac{-4-1}{4}~~}{2} \right)
\\\\\\
\left( \cfrac{~~\frac{23}{4}~~}{\frac{2}{1}}~~,~~\cfrac{~~\frac{-5}{4}~~}{\frac{2}{1}} \right)\implies \left( \cfrac{23}{8}~~,~-\cfrac{5}{8} \right)[/tex]
