Parallel and perpendicular lines on a plane

The slope-intercept equation can define the line on a plane

Suppose we have two lines with equations and .

For lines to be parallel it is needed that

For lines to be perpendicular it is needed that

This is quite easy for mental calculation, but lines also can be defined by more general form
and

Then, for lines to be parallel it is needed that

And for lines to be perpendicular it is needed that

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

Parallel and Perpendicular Lines

A1

B1

C1

A2

B2

C2

Calculate

The lines are parallel

 

The lines are perpendicular

 

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