Formulas & tables/Mathematics/Analytic geometry/Condition for perpendicular lines

Condition for perpendicular lines

a1⋅a2=−1a_1\cdot a_2=-1

Result unit: — (warunek)

What it describes

Two lines are perpendicular when the product of their slopes equals −1.

Symbols

a1,a2a_1, a_2
slopes of the lines

Where it comes from

Perpendicular lines have slopes whose product is −1-1 (each is the negative reciprocal of the other).

When to use it

Finding a perpendicular line; altitudes of a triangle.

Example

A line has a1=2a_1=2. Give the slope of the perpendicular line.
Substitutiona1⋅a2=−1a_1\cdot a_2=-1.
Resulta2=−12a_2=-\tfrac12.

Related formulas

Condition for parallel lines Slope from two points

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