Question 984199
The given line {{{y=-2x-5}}} can be represented as an ordered pair  (x, -2x-5), since y is equated to  the expression {{{-2x-5}}}.  What you really want is the point of intersection for {{{y=-2x-5}}} and the line from  (-6,2) perpendicular to {{{y=-2x-5}}}.  Then you want the distance between these two points.


Line with {{{m=1/2}}} containing point  (-6,2)?
Perpendicular lines in a plane have slopes which are negative reciprocal of each other.
{{{y-2=(1/2)(x-(-6))}}}, using point slope form.
{{{y=(1/2)x+2*6+2}}}
{{{y=x/2+14}}}


Intersection of {{{y=x/2+14}}} and {{{y=-2x-5}}} ?
{{{x/2+14=-2x-5}}}
{{{x+28=-4x-10}}}
{{{5x=-28-10}}}
{{{x=-38/5}}}
-
{{{y=51/5}}}


Distance Formula for distance between  (-38/5,51/5) and  (-6,2) ?
{{{highlight_green(sqrt((-6-(-38/5))^2+(2-51/5)^2))}}}
some simplification and computation still needed.