# Is the product of the slopes of $2$ perpendicular lines $-1$?

If I have $2$ lines$AB$ and $PQ$ perpendicular to each other drawn on a graph- then will the slope of $AB$ times the slope of $PQ$ be equal to $-1$?

i.e $$[(y2-y1)/(x2-x1)] \times [(b2-b1)/(a2-a1)] = -1 ?$$

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## 1 Answer

Yes, that is so. A small trigonometrical proof will be like this:

$$\tan( \theta + \frac{\pi}{2} ) = - \cot {\theta} = - \frac{1}{\tan{\theta}}$$

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So long as neither line is vertical, of course. – Cameron Buie Nov 4 '12 at 18:10
@CameronBuie I see what you did there. – hjpotter92 Nov 4 '12 at 18:27
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