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Parallel lines equations

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Midline Equation
x + y + = 0
2 points
(x1 , y1) ( ) (x2 , y2) ( )
Slope, Point
(xp , yp) ( ) Slope = Angle =
Distance
Given line equation
First parallel line equation
2nd parallel line equation
Degree Radian     

Distance and midline equation of 2 parallel lines

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Line 1 Equation
x + y + = 0
2 points
(x1 , y1) ( ) (x2 , y2) ( )
Slope, Point
(xp , yp) ( ) Slope = Angle =
Line 2 Equation
x + y + = 0
2 points
(x1 , y1) ( ) (x2 , y2) ( )
Slope, Point
(xp , yp) ( ) Slope = Angle =
Given line equation  L1
Given line equation  L2
Distance between the lines
Midline equation
Line geometry Solved example

Midline of two parallel lines summary

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Lines given by the equations:
Ax + By + C = 0
Dx + Ey + F = 0
Two lines are parallel if:AE = BD
The slope of this parallel line is:m = −A/B = −D/E
And the perpendicular slope is:M = B/A = E/D
The equation of the midline is given by:
Midline equation
The distance between these parallel lines is:
Distance between parallel lines
When A = D and B = E (parallel lines) then the distance equation become:
Distance
If the line is a vertical line (no value for y in the lines equations) than the midline equation is:
Equation of vertical midline
Lines given by the equations:
y = ax + b
y = cy + d
Two lines are parallel if:a = c
The slope of these parallel lines is:m = a = c
And the perpendicular slope is:M = − 1/a = − 1/c
The equation of the midline is given by: Midline equation
The distance between this parallel lines is: Distance between this parallel lines

Midline of two parallel lines - solved example

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Find the equation of the midline between the given lines    x + 2y − 4 = 0    and    x + 2y + 1 = 0
Both lines are parallel because:       1*2 − 2*1 = 0
The slope of the line is:   m = − 1/2 = − 0.5
Now we will find the y intercepts values of the lines
y intercept
The midpoint of this intercepts is a point located on the midline: Midpoint of the intercepts
The value of the midpoint  (xp , yp)  is:    (0 , 0.75)
And the midline equation is:       y = mx + yp − mxp = − 0.5x + 0.75 + 0.5*0 = − 0.5x + 0.75
And after multiplying all terms by 4 we get the midline equation:       2x + 4y − 3 = 0