SOLUTION: What is the shortest distance from the point (6, 0) to the line y = 2x-2? Express your answer in simplest radical form.

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Question 1069454: What is the shortest distance from the point (6, 0) to the line y = 2x-2? Express your answer in simplest radical form.
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Shortest distance is found using a line perpendicular to y=2x-2 that goes through (6,0).
Perpendicular lines have slopes that are negative reciprocals.
2%2Am%5B2%5D=-1
m%5B2%5D=-1%2F2
So, using the point-slope form,
y-0=-%281%2F2%29%28x-6%29
y=-x%2F2%2B3
Now find the intersection point of the two lines,
-x%2F2%2B3=2x-2
-%285%2F2%29x=-5
x=2
and
y=2%282%29-2
y=4-2
y=2
So find use the distance formula,
D%5E2=%286-2%29%5E2%2B%280-2%29%5E2
D%5E2=4%5E2%2B4
D%5E2=20
D=2sqrt%285%29
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Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
The above is correct.  However you may have studied another 
method, and perhaps this is the way you should do it:

The formula for the shortest distance from the point (x1,y1) to the line Ax+By+C=0 is:




The line's equation y = 2x-2 is equivalent to

              -2x + y + 2 = 0 and  

A = -2, B = 1, C = 2, x1 = 6, y1 = 0,



Edwin