SOLUTION: find the closest distance between the line Y=2x -4 and the point (5,-4)

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: find the closest distance between the line Y=2x -4 and the point (5,-4)      Log On


   

Question 840983: find the closest distance between the line Y=2x -4 and the point (5,-4)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The closest distance of a point to a line is a perpendicular line through that point.
Perpendicular slopes have the relationship,
m%5B1%5D%2Am%5B2%5D=-1
2%2Am%5B2%5D=-1
m%7B2%5D=-1%2F2
y=-%281%2F2%29x%2Bb+
Use the point to solve for b
-4=-%281%2F2%29%285%29%2Bb
b=-8%2F2%2B5%2F2
b=-3%2F2
.
.
y=-%281%2F2%29x-3%2F2
.
.