SOLUTION: Find the distance between the given two lines. y=-x+4; y=-x

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Question 1056091: Find the distance between the given two lines. y=-x+4; y=-x
Found 2 solutions by Boreal, Alan3354:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-x%2Cx%2C-x%2B4%29
Notice that the distance is a perpendicular line to y=-x+4 from the origin.
The line is the base of a triangle
Each leg is 4 units long.
The perpendicular is y=x
The distance is from (0,0) to (2,2). That is sqrt (4+4)=2 sqrt (2) or about 2.828 units.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the distance between the given two lines. y=-x+4; y=-x
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Pick a point on y = -x. (0,0) is good.
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The distance from a point (x,y) to a line ax + by + c = 0 is
|ax + by + c|/(sqrt(a^2 + b^2)
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y=-x+4 --> x + y - 4 = 0
d = |-4|/sqrt(1 + 1) = 4/sqrt(2)
d = 2sqrt(2)