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Question 225755: How do i find the distance between these two pair of parallel of lines using only this:
y = 2x + 2
y = 2x - 3
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How do i find the distance between these two pair of parallel of lines using only this:
y = 2x + 2
y = 2x - 3
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A = angle of lines with x-axis = arctan(m) = arctan(2)
A = angle of line perpendicular with y-axis
distance between y-intercepts = 5
d = 5*cos(arctan(2))
d = ~2.236 = sqrt(5)
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check:
line perpendicular thru (0,2):
m = -1/2
2 = (-1/2)*0 + b
y = -x/2 + 2
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y = 2x - 3
Solve for intersection
-x/2 + 2 = 2x - 3
-x+4 = 4x-6
5x = 10
x = 2
y = 1 --> (2,1)
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distance from (0,2) to (2,1)
s = sqrt(4 + 1)
s = sqrt(5)
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The distance between parallel lines is the distance between y-intercepts times the cosine of the arctan of the slope.
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