Question 1139586

use distance formula:

{{{d=sqrt((x-x[1])^2+(y-y[1])^2)}}}

given:
{{{P}}}=({{{3}}},{{{-8}}})=({{{x[1]}}},{{{y[1]}}})
{{{R}}}=({{{10}}},{{{y}}}) =({{{x}}},{{{y}}})
 the distance between points {{{P}}} and {{{R}}} is {{{d=25}}}

{{{25=sqrt((10-3)^2+(y-(-8))^2)}}}
{{{25=sqrt((7)^2+(y+8)^2)}}}
{{{25=sqrt(49+(y+8)^2)}}}.......square both sides
{{{25^2=49+(y+8)^2}}}......solve for {{{y}}}
{{{625-49=(y+8)^2}}}
{{{576=(y+8)^2}}}
{{{sqrt(576)=y+8}}}
{{{24-8=y}}}
{{{y=16}}}

=> answer: {{{R}}}=({{{10}}},{{{16}}}) which is located in the first quadrant