Question 859827
The question would be the same as, find the equation of the line perpendicular to {{{y=-2x-2}}} and containing the point (-6,-5); where do these lines intersect; and then use distance formula to find the distance from the intersection point to (-6,-5).


{{{y=(1/2)x+b}}} contains (-6,-5).
{{{b=y-(1/2)x}}}
{{{b=-6-(1/2)(-5)}}}
{{{b=-6+5/2}}}
{{{b=-12/2+5/2}}}
{{{b=-7/2}}}
{{{y=(1/2)x-7/2}}}


What is the intersection point of y=-2x-2 and y=(1/2)x-7/2 ?
{{{-2x-2=(1/2)x-7/2}}}
{{{-4x-4=x-7}}}
{{{-5x-4=-7}}}
{{{-5x=4-7=3}}}
{{{x=-3/5}}}
-
{{{y=-2(-3/5)-2=6/5-2}}}
{{{y=6/5-10/5}}}
{{{y=-4/5}}}
-
Intersection point is (-3/5, -4/5).


Distance from (-6,-5) to y=-2x-2 is:
{{{highlight(sqrt((-6-(-3/5))^2+(-5-(-4/5))^2))}}}