Question 988954
Is this a question of the distance between the point and the line?


Given line {{{y=-x+11}}}, and a line perpendicular to it would have slope {{{1}}}, which is negative reciprocal of {{{-1}}}.


Now, what is the equation for the line of slope -1 which goes through the given point (2,3)?
{{{y-3=1(x-2)}}}
{{{y=x-2+3}}}
{{{y=x+1}}}


FIND INTERSECTION POINT OF  {{{system(y=x+1,y=-x+11)}}}.
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Equating the two formulas for y,{{{x+1=-x+11}}}
{{{2x+1=11}}}
{{{2x=10}}}
{{{x=5}}}
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{{{y=x+1}}}
{{{y=5+1}}}
{{{y=6}}}
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Intersection point is  (5,6).


DISTANCE FROM (5,6) TO (2,3):
Plug the values into the Distance Formula and evaluate or compute.
{{{highlight(sqrt((5-2)^2+(6-3)^2))}}}
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