Question 1185691
Line AC is  {{{y=x/2+5}}}.

Line through B(2,-2) and perpendicular to line AC is,....   {{{y=-2x+2}}}.


Intersection point of these two lines on line AC is,.....   (-6/5, 22/5).



Shortest distance from B to line AC is the distance between B(2,-2) and (-6/5, 22/5).   You can use the Distance Formula.