What is the distance formula between 2 parallel lines? dont push yourselves if you can't answer this?
by 
kkmwolfram
ANSWERS: 3
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it is the square root of (x2-x1)squared + (y2-y1)squared
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Substitute a point on one line into the implicit equation for the other.
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vector calc based solution: first we define the lines L1: p1 + t*v1 L2: p2 + u*v1 where pi is a point, and v1 is a vector and t & u are time notice I only use v1, NOT v1 & v2. That's because it's the same vector (parallel lines) not this problem turns into finding the distance between p1 and L2 the smallest distance would be the length of a perpendicular from p1 to L2, intersecting at a point, g draw a (right) triangle with (p2,p1) being the hypotenuse, and (p1,g), (p2,g) beings legs we know (by pythagorous) (p2,p1)#(p2,p1) = (p1,g)#(p1,g) + (p2,g)#(p2,g), where '#' is being used as the dot operator (p2,p1) is known, since we defined the lines with that also, (p2,g) is the 'projection' of (p2,p1) onto v1- so to find it's distance take (p2,p1)#v@ where v@ is the 'unit vector' of v1- or more simply: v@ = v1/||v1|| now you have enough to solve for (p1,g)#(p1,g)!
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