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	Slopes of Perpendicular Lines
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	Roots - Radicals 1
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	Writing Linear Equations Using Slope and Point
	Factoring Trinomials with Leading Coefficient 1
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	Writing a Rational Expression in Lowest Terms
	Solving Quadratic Inequalities with a Sign Graph
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	The Square of a Binomial
	Properties of Negative Exponents
	Inverse Functions
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	Rotating an Ellipse
	Multiplying Numbers
	Linear Equations
	Solving Equations with One Log Term
	Combining Operations
	The Ellipse
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	Graphing Inequalities in Two Variables
	Solving Trigonometric Equations
	Adding and Subtracting Fractions
	Simple Trinomials as Products of Binomials
	Ratios and Proportions
	Solving Equations
	Multiplying and Dividing Fractions 2
	Rational Numbers
	Difference of Two Squares
	Factoring Polynomials by Grouping
	Solving Equations That Contain Rational Expressions
	Solving Quadratic Equations
	Dividing and Subtracting Rational Expressions
	Square Roots and Real Numbers
	Order of Operations
	Solving Nonlinear Equations by Substitution
	The Distance and Midpoint Formulas
	Linear Equations
	Graphing Using x- and y- Intercepts
	Properties of Exponents
	Solving Quadratic Equations
	Solving One-Step Equations Using Algebra
	Relatively Prime Numbers
	Solving a Quadratic Inequality with Two Solutions
	Quadratics
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	Factoring a Difference of Two Squares
	Straight Lines
	Solving Quadratic Equations by Factoring
	Graphing Logarithmic Functions
	Simplifying Expressions Involving Variables
	Adding Integers
	Decimals
	Factoring Completely General Quadratic Trinomials
	Using Patterns to Multiply Two Binomials
	Adding and Subtracting Rational Expressions With Unlike Denominators
	Rational Exponents
	Horizontal and Vertical Lines

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Slopes of Perpendicular Lines

Perpendicular lines intersect at a right angle.

If two nonvertical lines are perpendicular, then their slopes are negative reciprocals of each other.

That is, if the slope of one line is , then the slope of any perpendicular line is .

The product of the slopes of two perpendicular lines is -1.

Note: To find the negative reciprocal of a fraction, switch the numerator and the denominator and change the sign. For example, the negative reciprocal of is . The negative reciprocal of -3 is .

Example 1

Find the slope of a line perpendicular to the line that passes through the points (-4, 1) and (1, -2).

Solution

First, find the slope of the line through the given points.

Let (x₁, y₁) = (-4, 1) and (x₂, y₂) = (1, 2).	m
Substitute the values in the slope formula.
Simplify.

The slope of the line through (-4, 1) and (1, -2) is .

The negative reciprocal of is .

A line perpendicular to the line through (-4, 1) and (1, -2) has slope .

Example 2

Determine if line A is perpendicular to line B.

Solution

First, find the slope of each line.	m
For line A, we use the points (-4, -3) and (2, 4). The slope of line A is .
Next, find the slope of line B. We use the points (-3, 0) and (5, -6).
The slope of line B is .

The slopes,

and

, are not negative reciprocals so the lines are not perpendicular.

Be careful! The lines do look perpendicular. But the relationship between their slopes tells us the lines are not perpendicular.