# How do you determine if two lines are perpendicular?

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If the angle formed between the intersecting lines are 90o then the two lines are perpendicular.

Or

If the dot product of the two lines is zero.

Or (by Misacek01)

In analytical geometry, when the lines are defined by linear functions, you write the functions in the form y = ax + b, where x is the independent variable, y is the dependent variable, a,b are real-valued constants. So, you have two functions for the two lines:

y(1) = a(1)x(1) + b(1) ; y(2) = a(2)x(2) + b(2)

(the ones and twos are just indices, not powers or multipliers). Then, the two lines are perpendicular if and only if

a(1)a(2) = 1

(i.e. the constants before the x variable are mutually inverse numbers).

An exception from the above rule is the situation when at least one of the lines is "vertical" (i.e. of the form x = k, where k is a real constant), as such lines do not have a slope. (This is because slope is defined as tg(alpha), where alpha is the angle between the line and the x axis, which in the case of vertical line is 90°, and the tangent function (tg(x)) is not defined for the angle 90°.) In this case, this approach cannot be used. However, if one of the lines is of the form

x = k

then a line is perpendicular to it if and only if it is of the form

y = l

, where k,l are real constants.