Shortest Distance of Arbitrary Point from Line Calculator

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✖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%
✖X Coordinate of Arbitrary Point is the component along the x-axis of an arbitrary point in the two dimensional plane.ⓘ X Coordinate of Arbitrary Point [x_a]			+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%
✖Y Coordinate of Arbitrary Point is the component along the y-axis of an arbitrary point in the two dimensional plane.ⓘ Y Coordinate of Arbitrary Point [y_a]			+10% -10%
✖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%

✖Shortest Distance of a Point from Line is the perpendicular distance from one arbitrary point to the Line under consideration.ⓘ Shortest Distance of Arbitrary Point from Line [d]

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Formula

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Shortest Distance of Arbitrary Point from Line

Formula

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

Example

`"9.838699"="modulus"((("6"*"5")+("-3"*"-2")+"30")/sqrt((("6")^2)+(("-3")^2)))`

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Shortest Distance of Arbitrary Point from Line Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
d = modulus(((L_x*x_a)+(L_y*y_a)+c_Line)/sqrt((L_x^2)+(L_y^2)))
This formula uses 2 Functions, 6 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 a Point from Line - Shortest Distance of a Point from Line is the perpendicular distance from one arbitrary point to the Line under consideration.
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.
X Coordinate of Arbitrary Point - X Coordinate of Arbitrary Point is the component along the x-axis of an arbitrary point in the 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.
Y Coordinate of Arbitrary Point - Y Coordinate of Arbitrary Point is the component along the y-axis of an arbitrary point in the two dimensional plane.
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.

STEP 1: Convert Input(s) to Base Unit

X Coefficient of Line: 6 --> No Conversion Required
X Coordinate of Arbitrary Point: 5 --> No Conversion Required
Y Coefficient of Line: -3 --> No Conversion Required
Y Coordinate of Arbitrary Point: -2 --> No Conversion Required
Constant Term of Line: 30 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = modulus(((L_x*x_a)+(L_y*y_a)+c_Line)/sqrt((L_x^2)+(L_y^2))) --> modulus(((6*5)+((-3)*(-2))+30)/sqrt((6^2)+((-3)^2)))

Evaluating ... ...

d = 9.83869910099907

STEP 3: Convert Result to Output's Unit

9.83869910099907 --> No Conversion Required

FINAL ANSWER

9.83869910099907 ≈ 9.838699 <-- Shortest Distance of a Point from Line

(Calculation completed in 00.004 seconds)

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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 Arbitrary Point from Line 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 of Arbitrary Point from Line?

Shortest Distance of Arbitrary Point from Line calculator uses 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))) to calculate the Shortest Distance of a Point from Line, Shortest Distance of Arbitrary Point from Line formula is defined as the perpendicular distance from one arbitrary point to the Line under consideration. Shortest Distance of a Point from Line is denoted by d symbol.

How to calculate Shortest Distance of Arbitrary Point from Line using this online calculator? To use this online calculator for Shortest Distance of Arbitrary Point from Line, enter X Coefficient of Line (L_x), X Coordinate of Arbitrary Point (x_a), Y Coefficient of Line (L_y), Y Coordinate of Arbitrary Point (y_a) & Constant Term of Line (c_Line) and hit the calculate button. Here is how the Shortest Distance of Arbitrary Point from Line calculation can be explained with given input values -> 9.838699 = modulus(((6*5)+((-3)*(-2))+30)/sqrt((6^2)+((-3)^2))).

FAQ

What is Shortest Distance of Arbitrary Point from Line?

Shortest Distance of Arbitrary Point from Line formula is defined as the perpendicular distance from one arbitrary point to the Line under consideration and is represented as d = modulus(((L_x*x_a)+(L_y*y_a)+c_Line)/sqrt((L_x^2)+(L_y^2))) or 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))). 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 Coordinate of Arbitrary Point is the component along the x-axis of an arbitrary point in the 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, Y Coordinate of Arbitrary Point is the component along the y-axis of an arbitrary point in the two dimensional plane & 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.

How to calculate Shortest Distance of Arbitrary Point from Line?

Shortest Distance of Arbitrary Point from Line formula is defined as the perpendicular distance from one arbitrary point to the Line under consideration is calculated using 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))). To calculate Shortest Distance of Arbitrary Point from Line, you need X Coefficient of Line (L_x), X Coordinate of Arbitrary Point (x_a), Y Coefficient of Line (L_y), Y Coordinate of Arbitrary Point (y_a) & Constant Term of Line (c_Line). With our tool, you need to enter the respective value for X Coefficient of Line, X Coordinate of Arbitrary Point, Y Coefficient of Line, Y Coordinate of Arbitrary Point & Constant Term 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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