Question 890350
Line RS is {{{y-2=m(x-1)}}},
{{{y-2=((7-2)/(6-1))(x-1)}}}
{{{y-2=(5/5)(x-1)}}}
{{{y-2=x-1}}}
{{{y=x-1+2}}}
{{{y=x+1}}} which contains all general points, <b>(x,x+1)</b>.


Which points are on that line AND {{{3/4}}} of the distance from R to S?
{{{(3/4)sqrt((7-2)^2+(6-1)^2)=sqrt((x+1-2)^2+(x-1)^2)}}}---Use of Distance Formula
{{{(3/4)sqrt(25+25)=sqrt((x-1)^2+(x-1)^2)}}}
{{{(3/4)sqrt(2*25)=sqrt(2(x-1)^2)}}}
{{{5(3/4)sqrt(2)=(x-1)sqrt(2)}}}, which may be a oversimplification;
Divide both sides by {{{sqrt(2)}}}.
{{{(5*3)/4=x-1}}}
{{{x=15/4+4/4}}}
{{{x=19/4}}}----Seems to be the value needed.


Corresponding value for y:
{{{y=19/4+1}}}, just using the equation of line RS
{{{y=19/4+4/4}}}
{{{highlight(y=23/4)}}}----ANSWER