Find Perpendicular Line Calculator

Perpendicular Line Formula:

\[ \text{If original line: } y = m_1x + b_1 \] \[ \text{Perpendicular line: } y = m_2x + b_2 \] \[ \text{where } m_2 = -\frac{1}{m_1} \]

Perpendicular Line Equation:

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1. What is a Perpendicular Line?

A perpendicular line is a straight line that forms a right angle (90 degrees) with another line. In coordinate geometry, two lines are perpendicular if the product of their slopes is -1.

2. How to Find a Perpendicular Line

To find a line perpendicular to a given line and passing through a specific point:

\[ \text{Given line: } y = m_1x + b_1 \] \[ \text{Perpendicular slope: } m_2 = -\frac{1}{m_1} \] \[ \text{Equation: } y - y_1 = m_2(x - x_1) \]

3. Mathematical Principle

Key Concept: The slopes of perpendicular lines are negative reciprocals of each other. If one line has slope m, the perpendicular line has slope -1/m.

4. Using the Calculator

Instructions: Enter the slope of the original line and the coordinates of the point through which the perpendicular line must pass.

5. Frequently Asked Questions (FAQ)

Q1: What if the original line is horizontal?
A: The perpendicular line will be vertical (undefined slope), with equation x = constant.

Q2: What if the original line is vertical?
A: The perpendicular line will be horizontal (slope = 0), with equation y = constant.

Q3: Can two lines be perpendicular if one has slope 0?
A: Yes, a horizontal line (slope 0) is perpendicular to a vertical line (undefined slope).

Q4: How to verify if two lines are perpendicular?
A: Multiply their slopes - if the result is -1, they are perpendicular.

Q5: Does this work for 3D space?
A: No, this calculator is for 2D coordinate geometry only.