1. What is the Perpendicular Lines Equation?

The perpendicular lines equation calculates the slope of a line perpendicular to a given 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 lines formula:

Where:

• \( m_1 \) — Slope of the original line
• \( m_2 \) — Slope of the perpendicular line

Explanation: This formula shows that perpendicular lines have slopes that are negative reciprocals of each other. If one line has slope m, the perpendicular line has slope -1/m.

3. Importance of Perpendicular Slopes

Details: Understanding perpendicular slopes is crucial in geometry, engineering, architecture, and computer graphics. It's used in constructing right angles, designing orthogonal components, and creating coordinate systems.

4. Using the Calculator

Tips: Enter the slope of the original line. The slope cannot be zero (horizontal line) as the perpendicular would be vertical with undefined slope. All real numbers except zero are valid inputs.

5. Frequently Asked Questions (FAQ)

Q1: What happens if the original slope is zero?
A: If m1 = 0 (horizontal line), the perpendicular line is vertical with undefined slope. This calculator cannot handle vertical lines as their slope is undefined.

Q2: Are perpendicular slopes always negative reciprocals?
A: Yes, for two non-vertical lines to be perpendicular, their slopes must be negative reciprocals of each other.

Q3: What if both lines are vertical or horizontal?
A: Two vertical lines are parallel, not perpendicular. Two horizontal lines are also parallel. A vertical and horizontal line are perpendicular.

Q4: How do I find the equation of the perpendicular line?
A: Once you have the perpendicular slope m2, use point-slope form: y - y1 = m2(x - x1), where (x1, y1) is a point on the perpendicular line.

Q5: Does this work for all types of lines?
A: This works for all straight lines except when the original line is horizontal (m1=0) or the perpendicular line would be vertical (undefined slope).