We have to find the midpoint of the segment with the given endpoints

\(\displaystyle{\left(\frac{{3}}{{8}},-{\left(\frac{{2}}{{5}}\right)}\right.}\) and \(\displaystyle{\left(-{\left(\frac{{5}}{{2}}\right)},\frac{{3}}{{2}}\right)}\)

The midpoint of two points, (x1,y1) and (x2,y2) is the point M found by the following formula: \(\displaystyle{M}={\left(\frac{{{x}{1}+{x}{2}}}{{2}},\frac{{{y}{1}+{y}{2}}}{{2}}\right)}\)

By applying midpoint formula, the midpoint of the segment with the given endpoints \(\displaystyle{\left({x}{1},{y}{1}\right)}={\left(\frac{{3}}{{8}},-{\left(\frac{{2}}{{5}}\right)}\right.}\) and \(\displaystyle{\left({x}{2},{y}{2}\right)}={\left(-{\left(\frac{{5}}{{2}}\right)},\frac{{3}}{{2}}\right)}\) is given by

PSKM=((x1+x2)/2,(y1+y2)/2) =(((3/8)-(5/2)/2),-((2/5)+(3/2)/2)) =(((3/8)-(20/8)/2),-((4/10)+(15/10)/2)) =(-17/16,19/20)ZSK

\(\displaystyle{\left(\frac{{3}}{{8}},-{\left(\frac{{2}}{{5}}\right)}\right.}\) and \(\displaystyle{\left(-{\left(\frac{{5}}{{2}}\right)},\frac{{3}}{{2}}\right)}\)

The midpoint of two points, (x1,y1) and (x2,y2) is the point M found by the following formula: \(\displaystyle{M}={\left(\frac{{{x}{1}+{x}{2}}}{{2}},\frac{{{y}{1}+{y}{2}}}{{2}}\right)}\)

By applying midpoint formula, the midpoint of the segment with the given endpoints \(\displaystyle{\left({x}{1},{y}{1}\right)}={\left(\frac{{3}}{{8}},-{\left(\frac{{2}}{{5}}\right)}\right.}\) and \(\displaystyle{\left({x}{2},{y}{2}\right)}={\left(-{\left(\frac{{5}}{{2}}\right)},\frac{{3}}{{2}}\right)}\) is given by

PSKM=((x1+x2)/2,(y1+y2)/2) =(((3/8)-(5/2)/2),-((2/5)+(3/2)/2)) =(((3/8)-(20/8)/2),-((4/10)+(15/10)/2)) =(-17/16,19/20)ZSK