Find the distance between parallel lines
41－ 31 + 5 = 0 and 4x = 3y + 1 = 0
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Answer:
The method for calculating the distance between two parallel lines is as follows:
Ensure whether the equations of the given parallel lines are in slope-intercept form (y=mx+c).
The point of interception (c1 and c2) and slope value which is common for both the lines has to be determined.
After obtaining the above values, substitute them in the slope-intercept equation to find y.
Finally, put all the above values in the distance formula to find the distance between two parallel lines.
The two parallel lines can be taken in the form
y = mx + c1 … (i)
and y = mx + c2 … (ii)
The line (i) will intersect the x-axis at point A (–c1/m, 0) as shown in the figure.
Problems on Distance between Two Parallel Lines
The length of the perpendicular from point A to the line (ii) is of the same length as the distance between two lines.
Therefore, the distance between the lines (i) and (ii) is
|(–m)(–c1/m) + (–c2)|/√(1 + m2) or d = |c1–c2|/√(1+m2).
Distance d between two parallel lines y = mx + c1 and y = mx + c2 is given by
d = |C1–C2|/√A2 + B2
Distance formula d = |a1x1+b1y1+c1| / √a12+b12 , where d is the distance between two parallel lines. x1 and y1 are the two intersection points of the lines with the axis in a cartesian plane, while a1 and b1 are the coefficients of variable x and y of the line.
The equation of line through which equation of the distance formula is written as
a1x+b1y+c1 = 0
Considering the following equations of 2 parallel lines, we can calculate the distance between those lines using the distance formula
ax+by+c = 0
ax+by+c1 = 0
Using above 2 equations we can conclude that
Distance formula d = |c-c1| / √a2+b2
