Question

Find the point P on the line y=4x that is closes to the point (68,0). What is the least distance between P and (68,0)

Answer 1

line from line to point is perpendicular to original line :)
m' = -1/4
in
y = -x/4 + b
now through point
0 = -68/4 + b
b = 17
so
line to point is y = -x/4 + 17
where does it hit original line?
-x/4 + 17 = 4 x
-x + 68 = 16 x
17 x = 68
x = 4
so intersection at (4 , 16)
now how far is it from (4,16) to (68,0)
d^2 = 64^2 + 16^2

Answer 2

and check to see that the answer agrees with the formula giving the distance from a point (x,y) to the line Ax+By+C=0

d = |Ax+By+C|/√(A^2+B^2)