Shortest Distance between Parallel Lines Calculator

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✖Constant Term of First Line is the numerical value which is not a coefficient of x or y in the standard equation of the first Line among a pair of lines.ⓘ Constant Term of First Line [c₁]			+10% -10%
✖Constant Term of Second Line is the numerical value which is not a coefficient of x or y in the standard equation of the second Line among a pair of lines.ⓘ Constant Term of Second Line [c₂]			+10% -10%
✖X Coefficient of Line is the numerical coefficient of x in the standard equation of a Line ax+by+c=0 in two dimensional plane.ⓘ X Coefficient of Line [L_x]			+10% -10%
✖Y Coefficient of Line is the numerical coefficient of y in the standard equation of a Line ax+by+c=0 in two dimensional plane.ⓘ Y Coefficient of Line [L_y]			+10% -10%

✖Shortest Distance of Parallel Lines is the perpendicular distance between any pair of parallel Lines in two dimensional plane.ⓘ Shortest Distance between Parallel Lines [d_{Parallel Lines}]

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Formula

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Shortest Distance between Parallel Lines

Formula

`"d"_{"Parallel Lines"} = "modulus"("c"_{"1"}- ("c"_{"2"}))/sqrt(("L"_{"x"}^2)+("L"_{"y"}^2))`

Example

`"14.90712"="modulus"("-50"- ("50"))/sqrt((("6")^2)+(("-3")^2))`

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Shortest Distance between Parallel Lines Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shortest Distance of Parallel Lines = modulus(Constant Term of First Line- (Constant Term of Second Line))/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2))
d_{Parallel Lines} = modulus(c₁- (c₂))/sqrt((L_x^2)+(L_y^2))
This formula uses 2 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
modulus - Modulus of a number is the remainder when that number is divided by another number., modulus

Variables Used

Shortest Distance of Parallel Lines - Shortest Distance of Parallel Lines is the perpendicular distance between any pair of parallel Lines in two dimensional plane.
Constant Term of First Line - Constant Term of First Line is the numerical value which is not a coefficient of x or y in the standard equation of the first Line among a pair of lines.
Constant Term of Second Line - Constant Term of Second Line is the numerical value which is not a coefficient of x or y in the standard equation of the second Line among a pair of lines.
X Coefficient of Line - X Coefficient of Line is the numerical coefficient of x in the standard equation of a Line ax+by+c=0 in two dimensional plane.
Y Coefficient of Line - Y Coefficient of Line is the numerical coefficient of y in the standard equation of a Line ax+by+c=0 in two dimensional plane.

STEP 1: Convert Input(s) to Base Unit

Constant Term of First Line: -50 --> No Conversion Required
Constant Term of Second Line: 50 --> No Conversion Required
X Coefficient of Line: 6 --> No Conversion Required
Y Coefficient of Line: -3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_{Parallel Lines} = modulus(c₁- (c₂))/sqrt((L_x^2)+(L_y^2)) --> modulus((-50)- (50))/sqrt((6^2)+((-3)^2))

Evaluating ... ...

d_{Parallel Lines} = 14.9071198499986

STEP 3: Convert Result to Output's Unit

14.9071198499986 --> No Conversion Required

FINAL ANSWER

14.9071198499986 ≈ 14.90712 <-- Shortest Distance of Parallel Lines

(Calculation completed in 00.004 seconds)

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Credits

Created by Anamika Mittal

Vellore Institute of Technology (VIT), Bhopal

Anamika Mittal has created this Calculator and 50+ more calculators!

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

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< 3 Pair of Lines Calculators

Obtuse Angle between Pair of Lines

Go Obtuse Angle between Pair of Lines = pi-arctan(abs((Slope of Second Line-(Slope of First Line))/(1+(Slope of First Line)*Slope of Second Line)))

Shortest Distance between Parallel Lines

Go Shortest Distance of Parallel Lines = modulus(Constant Term of First Line- (Constant Term of Second Line))/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2))

Acute Angle between Pair of Lines

Go Acute Angle between Pair of Lines = arctan(abs((Slope of Second Line-(Slope of First Line))/(1+(Slope of First Line)*Slope of Second Line)))

Shortest Distance between Parallel Lines Formula

What is a Line?

A Line in two dimensional plane is the infinite extension of the line segment joining two arbitrary points, in both directions. In a Line for any two arbitrary points, the ratio of difference of y coordinates to the difference of x coordinates in a specific order is a constant value. That value is called the slope of that Line. Every Line has a slope, which can be any real number - positive or negative or zero.

How to Calculate Shortest Distance between Parallel Lines?

Shortest Distance between Parallel Lines calculator uses Shortest Distance of Parallel Lines = modulus(Constant Term of First Line- (Constant Term of Second Line))/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2)) to calculate the Shortest Distance of Parallel Lines, Shortest Distance between Parallel Lines formula is defined as the perpendicular distance between any pair of Parallel Lines in two dimensional plane. Shortest Distance of Parallel Lines is denoted by d_{Parallel Lines} symbol.

How to calculate Shortest Distance between Parallel Lines using this online calculator? To use this online calculator for Shortest Distance between Parallel Lines, enter Constant Term of First Line (c₁), Constant Term of Second Line (c₂), X Coefficient of Line (L_x) & Y Coefficient of Line (L_y) and hit the calculate button. Here is how the Shortest Distance between Parallel Lines calculation can be explained with given input values -> 14.90712 = modulus((-50)- (50))/sqrt((6^2)+((-3)^2)).

FAQ

What is Shortest Distance between Parallel Lines?

Shortest Distance between Parallel Lines formula is defined as the perpendicular distance between any pair of Parallel Lines in two dimensional plane and is represented as d_{Parallel Lines} = modulus(c₁- (c₂))/sqrt((L_x^2)+(L_y^2)) or Shortest Distance of Parallel Lines = modulus(Constant Term of First Line- (Constant Term of Second Line))/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2)). Constant Term of First Line is the numerical value which is not a coefficient of x or y in the standard equation of the first Line among a pair of lines, Constant Term of Second Line is the numerical value which is not a coefficient of x or y in the standard equation of the second Line among a pair of lines, X Coefficient of Line is the numerical coefficient of x in the standard equation of a Line ax+by+c=0 in two dimensional plane & Y Coefficient of Line is the numerical coefficient of y in the standard equation of a Line ax+by+c=0 in two dimensional plane.

How to calculate Shortest Distance between Parallel Lines?

Shortest Distance between Parallel Lines formula is defined as the perpendicular distance between any pair of Parallel Lines in two dimensional plane is calculated using Shortest Distance of Parallel Lines = modulus(Constant Term of First Line- (Constant Term of Second Line))/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2)). To calculate Shortest Distance between Parallel Lines, you need Constant Term of First Line (c₁), Constant Term of Second Line (c₂), X Coefficient of Line (L_x) & Y Coefficient of Line (L_y). With our tool, you need to enter the respective value for Constant Term of First Line, Constant Term of Second Line, X Coefficient of Line & Y Coefficient of Line and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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