homechevron_rightProfessionalchevron_rightEngineering

Parallel and perpendicular lines on a plane

This online calculator checks lines' slopes to see if they are parallel or perpendicular

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

PLANETCALC, Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

The lines are parallel
 
The lines are perpendicular
 
Save the calculation to reuse next time, to extension embed in your website or share share with friends.

Comments