SOLUTION: What is the shortest distance between 2 parallel lines given 2x+y-2=0 and 2x+y-3=0 ?

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Question 932465: What is the shortest distance between 2 parallel lines given 2x+y-2=0 and 2x+y-3=0 ?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
In slope intercept form, the equations are,
y=-2x%2B2
y=-2x%2B3
The line perpendicular to these two lines would have the slope 1%2F2 since perpendicular lines have slopes that are negative reciprocals.
The slope also equals the tangent of the angle the line makes with the x-axis.

So now you have a right triangle.

You know that
tan%28a%29=1%2F2
From the diagram,
cos%28a%29=d%2F%281%2F2%29
cos%28a%29=2d
sin%28a%29=tan%28a%29%2Acos%28a%29
sin%28a%29=%281%2F2%29%282d%29
sin%28a%29=d
And you know,
sin%28a%29%5E2%2Bcos%28a%29%5E2=1
d%5E2%2B4d%5E2=1
5d%5E2=1
d%5E2=1%2F5
d=1%2Fsqrt%285%29
highlight%28d=sqrt%285%29%2F5%29