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Perpendicular Slope Formula:
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A perpendicular slope is the negative reciprocal of the original slope. If two lines are perpendicular, the product of their slopes equals -1. This relationship is fundamental in coordinate geometry and linear algebra.
The calculator uses the perpendicular slope formula:
Where:
Explanation: The negative reciprocal relationship ensures that the two lines intersect at a 90-degree angle, forming perpendicular lines.
Details: Understanding perpendicular slopes is essential in geometry, engineering, architecture, and computer graphics. It's used to construct right angles, design orthogonal components, and solve geometric problems involving perpendicular relationships.
Tips: Enter the original slope value. The slope cannot be zero (as division by zero is undefined). The calculator will compute the perpendicular slope, which is the negative reciprocal of the input value.
Q1: What happens if the original slope is zero?
A: A slope of zero represents a horizontal line. Its perpendicular would be a vertical line with an undefined slope, which cannot be calculated using this formula.
Q2: What if the original slope is undefined?
A: An undefined slope represents a vertical line. Its perpendicular would be a horizontal line with a slope of zero.
Q3: Can this be used for 3D geometry?
A: This formula applies to 2D coordinate geometry. In 3D, perpendicular relationships are more complex and involve vector dot products.
Q4: What's the relationship between perpendicular slopes?
A: If two lines are perpendicular, the product of their slopes equals -1 (m₁ × m₂ = -1).
Q5: How is this used in real-world applications?
A: Perpendicular slopes are used in construction for creating right angles, in computer graphics for orthogonal projections, and in navigation for calculating perpendicular courses.