Question 1145847

The midpoint of ({{{UV}}}) ̅ is ({{{6}}}, {{{7}}}). 
({{{x}}},{{{y}}}) = ({{{6}}}, {{{7}}})

The coordinates of one endpoint are U({{{3}}}, {{{-5}}}). 
({{{x[1]}}},{{{y[1]}}}) = ({{{3}}},{{{ -5}}})


 the coordinates of endpoint V are ({{{x[2]}}},{{{y[2]}}})


sketch looks like this:
{{{U}}}--------------------------------------------{{{M}}}--------------------------------------------{{{V}}}
or
({{{x[1]}}},{{{y[1]}}}) --------------------------------({{{x}}},{{{y}}}) ---------------------------------------({{{x[2]}}},{{{y[2]}}}) 


we know that

({{{3}}}, {{{-5}}})----------------------------------- ({{{6}}}, {{{7}}})-----------------------------------({{{x[2]}}},{{{y[2]}}})


as you know the midpoint of ({{{UV}}}) coordinates are 

({{{6}}}, {{{7}}})=({{{x}}},{{{y}}})=({{{x[1]+x[2])/2}}},({{{y[1]+y[2])/2}}})

since {{{x=6}}}, {{{x[1]=3}}}, {{{y=7}}}, {{{y[1]=-5}}}, we have:


{{{(x[1]+x[2])/2=6}}} =>{{{x[1]+x[2]=12}}}=>{{{x[2]=12-x[1]}}} =>{{{x[2]=12-3}}}=>{{{x[2]=9}}}

{{{(y[1]+y[2])/2=7}}}=>{{{y[1]+y[2]=14}}} =>{{{y[2]=14-y[1]}}}=>{{{y[2]=14-(-5)}}}=>{{{y[2]=14+5}}}=>{{{y[2]=12}}}

so,  the coordinates of endpoint {{{V}}} are ({{{x[2]}}},{{{y[2]}}})=({{{9}}},{{{19}}})