HARD Calculus hwk question.?

Question

Calculus hwk help?
Use the first derivative test to show that the shortest distance from a point (P,Q) to the line ax+by+c=0 is

d= l aP+bQ+c l/ sqrt(a^2+b^2)

(assuming (P, Q) is NOT on the line)

I dont even know where to start...

proffessor mentioned we needed to treat the y in the distance formula as a function then substittue that in for the numerator of the implicit derivative plus the x and y and solve however that is not giving me the answer.

Answer 1

The shortest distance from a point to a line is a line perpendicular to that line. (Perpendicular lines have slopes that are negative reciprocals of each other.)

Now to prove that:
Write an equation for the distance from (P,Q) to any arbitrary point (x,y). Then take the derivative and set to zero.