Distance and midline equation of 2 parallel lines Print Distance and midline equation of 2 parallel lines summary
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 =
Distance between the lines
Midline equation
Parallel lines equations Print parallel lines equations summary
Midline Equation
x + y + = 0
2 points
(x1 , y1) ( ) (x2 , y2) ( )
Slope, Point
(xp , yp) ( ) Slope = Angle =
Distance
First parallel line equation
2nd parallel line equation
Degree Radian     
Line geometry Solved example
Midline of two parallel lines Print midline of two parallel lines summary
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 lines 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 this 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 this 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 Print solved example
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