Question 714836
gien: {{{M}}}({{{6}}}, {{{6}}}) is the midpoint of {{{SR}}}

the coordinates of {{{S}}} are ({{{8}}}, {{{9}}})

find:  the coordinates of {{{R}}}


The midpoint 

{{{M }}} coordinates are: ({{{x}}}, {{{y}}})= ({{{(x1+x2)/2}}},{{{(y1+y2)/2}}})

plug in given coordinates of the midpoint which are ({{{6}}}, {{{6}}}) and also a point {{{S}}} to be ({{{8}}}, {{{9}}})

({{{6}}}, {{{6}}})= ({{{(x1+8)/2}}},{{{(y1+9)/2}}})




We now equate {{{(x + 8)/2}}} to {{{6}}} and solve for {{{x}}} and then we equate {{{(y + 9)/2}}} to {{{6}}} and solve for {{{y}}}.

{{{(x + 8)/2 = 6}}}......multiply both sides by {{{2}}}

{{{x + 8 = 6*2}}}

{{{x + 8 = 12}}}

{{{x = 12 - 8}}}

{{{x = 4}}}



now we do the same for {{{y}}}

{{{(y + 9)/2 = 6}}}

{{{y + 9 = 6*2}}}

{{{y + 9 = 12}}}

{{{y = 12 - 9}}}

{{{y = 3}}}

so, the coordinates of point {{{R}}} are ({{{4}}}, {{{3}}})


check:

*[invoke midpoint 4, 3, 8, 9]