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Perpendicular Slope Formula:
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The Perpendicular Slope Calculator determines the slope of a line perpendicular to a given line. In geometry, perpendicular lines intersect at a 90-degree angle, and their slopes are negative reciprocals of each other.
The calculator uses the perpendicular slope formula:
Where:
Explanation: The negative reciprocal relationship ensures that the product of the original slope and the perpendicular slope equals -1 (m × m⊥ = -1), which is the condition for perpendicularity in the Cartesian coordinate system.
Details: Calculating perpendicular slopes is essential in geometry, trigonometry, and various engineering applications. It's used to find equations of perpendicular lines, determine right angles in construction, and solve problems in coordinate geometry.
Tips: Enter the original slope value. The slope can be any real number except zero (as division by zero is undefined). The calculator will return the negative reciprocal of the input value.
Q1: What if the original slope is zero?
A: If the original slope is zero, the perpendicular slope would be undefined (division by zero), representing a vertical line.
Q2: What if the original slope is undefined (vertical line)?
A: If the original line is vertical (undefined slope), the perpendicular line will be horizontal with a slope of zero.
Q3: Can the perpendicular slope be the same as the original slope?
A: No, except in the special case where the original slope is i or -i (imaginary numbers), which doesn't occur in real-number coordinate systems.
Q4: How is this used in real-world applications?
A: Perpendicular slope calculations are used in construction for creating right angles, in computer graphics for generating orthogonal vectors, and in navigation for plotting perpendicular courses.
Q5: What's the relationship between perpendicular slopes and angles?
A: Lines are perpendicular if the product of their slopes equals -1. This relationship comes from the trigonometric identity tan(θ) × tan(θ+90°) = -1.