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Shortest Distance between Parallel Lines Formula

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Shortest Distance of Parallel Lines is the perpendicular distance between any pair of parallel Lines in two dimensional plane. Check FAQs

d Parallel Lines = mod \underset{̲}{u} s \frac{c 1 - (c 2)}{\sqrt{({L x}^{2}) + ({L y}^{2})}}

d_{Parallel Lines} - Shortest Distance of Parallel Lines?c₁ - Constant Term of First Line?c₂ - Constant Term of Second Line?L_x - X Coefficient of Line?L_y - Y Coefficient of Line?

Shortest Distance between Parallel Lines Example

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Here is how the Shortest Distance between Parallel Lines equation looks like with Values.

Here is how the Shortest Distance between Parallel Lines equation looks like with Units.

Here is how the Shortest Distance between Parallel Lines equation looks like.

14.9071 = mod \underset{̲}{u} s \frac{-50 - (50)}{\sqrt{(6^{2}) + ({-3}^{2})}}

14.9071 = mod \underset{̲}{u} s \frac{-50 - (50)}{\sqrt{(6^{2}) + ({-3}^{2})}}

14.9071 = mod \underset{̲}{u} s \frac{-50 - (50)}{\sqrt{(6^{2}) + ({-3}^{2})}}

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Shortest Distance between Parallel Lines Solution

Follow our step by step solution on how to calculate Shortest Distance between Parallel Lines?

FIRST Step Consider the formula

d Parallel Lines = mod \underset{̲}{u} s \frac{c 1 - (c 2)}{\sqrt{({L x}^{2}) + ({L y}^{2})}}

Next Step Substitute values of Variables

∴

d Parallel Lines = mod \underset{̲}{u} s \frac{-50 - (50)}{\sqrt{(6^{2}) + ({-3}^{2})}}

Next Step Prepare to Evaluate

∴

d Parallel Lines = mod \underset{̲}{u} s \frac{-50 - (50)}{\sqrt{(6^{2}) + ({-3}^{2})}}

Next Step Evaluate

∴

d Parallel Lines = 14.9071198499986

LAST Step Rounding Answer

∴

d Parallel Lines = 14.9071

Shortest Distance between Parallel Lines Formula Elements

Variables

Functions

Shortest Distance of Parallel Lines

Shortest Distance of Parallel Lines is the perpendicular distance between any pair of parallel Lines in two dimensional plane.

Symbol: d_{Parallel Lines}

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Shortest Distance of Parallel Lines

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.

Symbol: c₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant Term of First Line

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.

Symbol: c₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant Term of Second Line

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.

Symbol: L_x

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find X Coefficient of Line

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.

Symbol: L_y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Y Coefficient of Line

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.

Syntax: sqrt(Number)

modulus

Modulus of a number is the remainder when that number is divided by another number.

Syntax: modulus

Other formulas in Pair of Lines category

Go Obtuse Angle between Pair of Lines

∠ Obtuse = π - \arctan (| \frac{m 2 - (m 1)}{1 + (m 1) \cdot m 2} |)

Go Acute Angle between Pair of Lines

∠ Acute = \arctan (| \frac{m 2 - (m 1)}{1 + (m 1) \cdot m 2} |)

How to Evaluate Shortest Distance between Parallel Lines?

Shortest Distance between Parallel Lines evaluator 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 evaluate 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 evaluate Shortest Distance between Parallel Lines using this online evaluator? To use this online evaluator 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.

FAQs on Shortest Distance between Parallel Lines

What is the formula to find Shortest Distance between Parallel Lines?

The formula of Shortest Distance between Parallel Lines is expressed as 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)). Here is an example- 14.90712 = modulus((-50)-(50))/sqrt((6^2)+((-3)^2)).

How to calculate Shortest Distance between Parallel Lines?

With Constant Term of First Line (c₁), Constant Term of Second Line (c₂), X Coefficient of Line (L_x) & Y Coefficient of Line (L_y) we can find Shortest Distance between Parallel Lines using the formula - 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)). This formula also uses Square Root (sqrt), Modulus (modulus) function(s).

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Shortest Distance between Parallel Lines Formula

Shortest Distance between Parallel Lines Example

Shortest Distance between Parallel Lines Solution

Shortest Distance between Parallel Lines Formula Elements

Other formulas in Pair of Lines category

How to Evaluate Shortest Distance between Parallel Lines?

FAQs on Shortest Distance between Parallel Lines

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