Perpendicular Line Calculator

To find the equation of a perpendicular line, determine the negative reciprocal of the slope of the original line and use it with a point to calculate the new line equation.

Perpendicular Line Calculator

Original Line Slope (m) Original y-Intercept (b) X-Coordinate of Perpendicular Line Y-Coordinate of Perpendicular Line

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The Perpendicular Line Calculator is a versatile tool for determining the equation of a line perpendicular to a given line. By inputting the original line’s slope and a specific point, users can calculate the perpendicular line’s slope and equation.

This tool is especially helpful in geometry, physics, and engineering, where perpendicularity is essential for analysis and design. It ensures precision and saves time when solving problems involving intersecting lines.

Formula

$y = mx + b$​

Variable	Description
y	Dependent variable (y-coordinate)
m	Slope of the line
x	Independent variable (x-coordinate)
b	Y-intercept of the line
m_2	Slope of the perpendicular line

Solved Calculations

Example 1:
Find the perpendicular line equation for $y = 2x + 3$ passing through the point (4, 5).

Step	Calculation	Result
Original Slope ($m_1$)	$2$
Perpendicular Slope ($m_2$)	$m_2 = -1/m_1 = -1/2$	$-1/2$
Substitute in $y = mx + b$	$5 = (-1/2)(4) + b$	$5 = -2 + b$
Solve for $b$	$b = 7$
Final Equation	$y = -1/2x + 7$

 

Example 2:
Determine the perpendicular line to $y = -3x + 2$ that passes through the point (1, -2).

Step	Calculation	Result
Original Slope ($m_1$)	$-3$
Perpendicular Slope ($m_2$)	$m_2 = -1/m_1 = 1/3$	$1/3$
Substitute in $y = mx + b$	$-2 = (1/3)(1) + b$	$-2 = 1/3 + b$
Solve for $b$	$b = -2 – 1/3 = -7/3$
Final Equation	$y = 1/3x – 7/3$

What is the Perpendicular Line Calculator?

The Perpendicular Line Calculator is a valuable tool. One can use it for finding the equation of a line that is perpendicular to a given line.

By using the slope of the original line and applying the concept that the product of the slopes of perpendicular lines is -1, this calculator provides the perpendicular line’s equation in slope-intercept or point-slope form. It’s particularly useful for geometry, algebra, and real-world applications involving perpendicular relationships.

This tool answers queries like “How do I find the equation of a perpendicular line?” or “What is the slope of a line perpendicular to a given slope?”

It also calculates perpendicular lines passing through a specific point or even in 3D space. Whether working with points, slopes, or equations, the calculator ensures precise results for all scenarios.

Final Words:

To sum up, the Perpendicular Line Calculator is an efficient and reliable solution for solving perpendicular line equations. It simplifies complex geometric and algebraic computations, making it an indispensable resource for students, teachers, and professionals.