Lines and Slope  Chameleon Home  Ask Dr. Math 

Perpendicular Lines These two lines are perpendicular: they meet at a 90° angle. We could try to check whether or not these lines are really perpendicular by using a protractor, but it's hard to measure a picture on a computer monitor without making mistakes. Can we find out whether lines are perpendicular without measuring their angles? Let's start by comparing the slope of these lines. m = (y_{2}  y_{1}) / (x_{2}  x_{1})
The slope of the blue line is 4, and the slope of the red line is 1/4. Do these numbers have anything in common? You might notice that
If we multiply both sides of the equation by m_{blue}, we get
Taking the opposite of both sides tells us that
The product of the slopes of our lines is 1. In fact, the product of the slopes of any pair of perpendicular lines is 1. So if we have any two perpendicular lines, we can call their slopes m_{1} and m_{2} and write this fact as an equation: We can use this equation to check whether or not two lines are perpendicular without trying to measure the angle between them. (Unfortunately, this won't work for vertical lines, because they don't have slopes. Just remember that vertical lines are perpendicular to lines with slopes of 0.) 
Please send questions, comments, and suggestions
to Ursula Whitcher
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