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Parallel and perpendicular lines on a plane

This online calculator checks lines' slopes to see if they are parallel or perpendicular
Timur2011-07-30 08:52:02

This page exists due to effort of the following persons:

The line on a plane can be defined by the slope-intercept equation
y=kx+b

Suppose we have two lines with equations y=k_1x+b_1 and y=k_2x+b_2.

For lines to be parallel it is needed that
k_1=k_2 , b_1 <> b_2

For lines to be perpendicular it is needed that
k_1k_2=-1

This is quite easy for mental calculation, but lines also can be defined by more general form
A_1x+B_1y+C_1=0 and A_2x+B_2y+C_2=0

Then, for lines to be parallel it is needed that
\frac{A_1}{A_2}=\frac{B_1}{B_2} <> \frac{C_1}{C_2}

And for lines to be perpendicular is it needed that
A_1A_2+B_1B_2=0

So, the calculator below frees you from converting this to slope-intercept form and checks if lines are parallel or perpendicular

Parallel and Perpendicular LinesCreative Commons Attribution/Share-Alike License 3.0 (Unported)
 
 

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