perplexus.info :: Geometry : Slope products

Slope products (Posted on 2011-11-08)

It is a well known result from algebra that if two lines are perpendicular then the product of their slopes is always -1.^*

Give a very simple proof that if the lines form any angle besides 90^o the product of the slopes cannot be a constant.

^*Assuming neither line is vertical.

Submitted by Jer

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Solution: (Hide)

My solution: 90^o is the only angle that guarantees the lines will have opposite signs. For any smaller angle it is possible that both slopes be positive or that one is positive and the other negative.
There are other nice arguments in the comments.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Solution	Ady TZIDON	2011-11-09 03:55:20
Solution	Paul	2011-11-08 18:56:41
solution	Charlie	2011-11-08 13:03:17

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