Shortest Distance of Line from Origin Calculator

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✖Constant Term of Line is the numerical value which is not a coefficient of x or y in the standard equation of a Line ax+by+c=0 in two dimensional plane.ⓘ Constant Term of Line [c_Line]			+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 Line from Origin is the perpendicular distance between a Line in two dimensional plane and the origin.ⓘ Shortest Distance of Line from Origin [d_Origin]

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Formula

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Shortest Distance of Line from Origin

Formula

`"d"_{"Origin"} = "modulus"("c"_{"Line"}/sqrt(("L"_{"x"}^2)+("L"_{"y"}^2)))`

Example

`"4.472136"="modulus"("30"/sqrt((("6")^2)+(("-3")^2)))`

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Shortest Distance of Line from Origin Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shortest Distance of Line from Origin = modulus(Constant Term of Line/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2)))
d_Origin = modulus(c_Line/sqrt((L_x^2)+(L_y^2)))
This formula uses 2 Functions, 4 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 Line from Origin - Shortest Distance of Line from Origin is the perpendicular distance between a Line in two dimensional plane and the origin.
Constant Term of Line - Constant Term of Line is the numerical value which is not a coefficient of x or y in the standard equation of a Line ax+by+c=0 in two dimensional plane.
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 Line: 30 --> 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_Origin = modulus(c_Line/sqrt((L_x^2)+(L_y^2))) --> modulus(30/sqrt((6^2)+((-3)^2)))

Evaluating ... ...

d_Origin = 4.47213595499958

STEP 3: Convert Result to Output's Unit

4.47213595499958 --> No Conversion Required

FINAL ANSWER

4.47213595499958 ≈ 4.472136 <-- Shortest Distance of Line from Origin

(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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< 4 Line Calculators

Shortest Distance of Arbitrary Point from Line

Go Shortest Distance of a Point from Line = modulus(((X Coefficient of Line*X Coordinate of Arbitrary Point)+(Y Coefficient of Line*Y Coordinate of Arbitrary Point)+Constant Term of Line)/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2)))

Shortest Distance of Line from Origin

Go Shortest Distance of Line from Origin = modulus(Constant Term of Line/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2)))

Number of Straight Lines using Non Collinear Points

Go Number of Straight Lines = C(Number of Non Collinear Points,2)

X Coefficient of Line given Slope

Go X Coefficient of Line = -(Y Coefficient of Line*Slope of Line)

Shortest Distance of Line from Origin Formula

Shortest Distance of Line from Origin = modulus(Constant Term of Line/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2)))
d_Origin = modulus(c_Line/sqrt((L_x^2)+(L_y^2)))

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 of Line from Origin?

Shortest Distance of Line from Origin calculator uses Shortest Distance of Line from Origin = modulus(Constant Term of Line/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2))) to calculate the Shortest Distance of Line from Origin, Shortest Distance of Line from Origin formula is defined as the perpendicular distance between a Line in two dimensional plane and the origin. Shortest Distance of Line from Origin is denoted by d_Origin symbol.

How to calculate Shortest Distance of Line from Origin using this online calculator? To use this online calculator for Shortest Distance of Line from Origin, enter Constant Term of Line (c_Line), X Coefficient of Line (L_x) & Y Coefficient of Line (L_y) and hit the calculate button. Here is how the Shortest Distance of Line from Origin calculation can be explained with given input values -> 4.472136 = modulus(30/sqrt((6^2)+((-3)^2))).

FAQ

What is Shortest Distance of Line from Origin?

Shortest Distance of Line from Origin formula is defined as the perpendicular distance between a Line in two dimensional plane and the origin and is represented as d_Origin = modulus(c_Line/sqrt((L_x^2)+(L_y^2))) or Shortest Distance of Line from Origin = modulus(Constant Term of Line/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2))). Constant Term of Line is the numerical value which is not a coefficient of x or y in the standard equation of a Line ax+by+c=0 in two dimensional plane, 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 of Line from Origin?

Shortest Distance of Line from Origin formula is defined as the perpendicular distance between a Line in two dimensional plane and the origin is calculated using Shortest Distance of Line from Origin = modulus(Constant Term of Line/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2))). To calculate Shortest Distance of Line from Origin, you need Constant Term of Line (c_Line), 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 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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