Question 976708
{{{y=((2+5)/(-4-3))x+b}}}
{{{y=-x+b}}}, slope being negative one.
{{{y=-x+(2+1*(-4))}}}
{{{highlight_green(y=-x-2)}}}, your line for the first two given points.


The line perpendicular through P is  {{{y-2=1(x-1)}}}
{{{y=x-1+2}}}
{{{highlight_green(y=x+1)}}}, the perpendicular line through P.


{{{-x-2=x+1}}}
{{{-2x=1+2}}}
{{{2x=-3}}}
{{{x=-3/2}}}
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{{{y=-3/2+1}}}
{{{y=-3/2+2/2}}}
{{{y=-1/2}}}
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Point on the first line where the perpendicular line intersects is  ( -3/2, -1/2 ).


What is the distance between (1,2) and (-3/2,-1/2) ?
Use the Distance Formula.