Perpendicular Line Calculator

Perpendicular Line Equation:

\[ y - y_1 = m_{\perp} (x - x_1) \] \[ m_{\perp} = -\frac{1}{m} \]

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 equals -1.

2. How Does the Calculator Work?

The calculator uses the perpendicular line equation:

\[ y - y_1 = m_{\perp} (x - x_1) \] \[ m_{\perp} = -\frac{1}{m} \]

Where:

\( m \) — Slope of the original line
\( m_{\perp} \) — Slope of the perpendicular line
\( (x_1, y_1) \) — Point through which the perpendicular line passes

Explanation: The perpendicular slope is the negative reciprocal of the original slope. If the original slope is undefined (vertical line), the perpendicular line will be horizontal, and vice versa.

3. Importance of Perpendicular Lines

Details: Perpendicular lines are fundamental in geometry, architecture, engineering, and computer graphics. They are used in constructing right angles, designing orthogonal systems, and solving geometric problems involving distances and angles.

4. Using the Calculator

Tips: Enter the slope of the original line and the coordinates of the point through which the perpendicular line should pass. The slope cannot be zero (horizontal line) for this calculation.

5. Frequently Asked Questions (FAQ)

Q1: What if the original line is horizontal (m=0)?
A: If the original line is horizontal, the perpendicular line will be vertical with an undefined slope. This calculator handles non-zero slopes.

Q2: What if the original line is vertical?
A: If the original line is vertical (undefined slope), the perpendicular line will be horizontal with slope 0.

Q3: Can I find perpendicular lines in 3D space?
A: This calculator is for 2D coordinate geometry. In 3D, perpendicularity involves vector dot products and is more complex.

Q4: How accurate are the results?
A: The results are mathematically exact based on the input values. The calculator provides rounded values for display purposes.

Q5: What applications use perpendicular lines?
A: Architecture (right angles in buildings), engineering (orthogonal components), computer graphics (coordinate systems), and navigation (grid systems).