﻿ Parallel lines
 Distance and midline equation of 2 parallel lines ▲
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 ▲
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
 Line geometry Solved example
 Midline of two parallel lines ▲
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: The distance between this parallel lines is: When A = D and B = E (parallel lines) then the distance equation become: If the line is a vertical line (no value for y in the lines equations) than the midline equation is: 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: The distance between this parallel lines is: Midline of two parallel lines - 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 The midpoint of this intercepts is a point located on the midline: 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