John walks along the edge of the field from point A to point C. If P is
the point on AC when John is nearest to point B, find the length of BP.
I suspect you tried to paste a picture here.
That will not work. I do not see it.
However
you need the line perpendicular to AC through point B
If you have AC in algebra
y = m x + b
then the slope of BP is
m' = -1/m and it goes through B
so find
y = m' x + b' for BP
solve for intersection of BP and AC, that is P
Now you can find |BP| the distance between B and P
sqrt (change in x^2 + change in y^2)