Question 1067344
The slope of your GIVEN line is {{{-5/2}}}.
The slope of the line you want to find must have slope  {{{2/5}}}.


WHY?  The two lines intersect at some point which you will find.  Then use Distance formula to find the length from the intersection point to point A(15,-21).   You are first looking for the line perpendicular to the given one which contains point A.


Line you want:
{{{y-(-21)=(2/5)(x-15)}}}, using point-slope form
{{{y+21=(2/5)x-6}}}
{{{highlight_green(y=(2/5)x-27)}}}



Now find intersection point of {{{5x+2y=4}}} and {{{y=(2/5)x-27}}}.
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Can you finish this?