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Presentation transcript:

Loci

A story about Ants… An army of ants work very hard all day long. They do everything their boss tells them, all the time. Every now and then he barks a random order at them just because he can. If the ants hear the boss’ order, they must obey The boss’ voice travels exactly 1metre from where he stands Where are the ants safe to stand to avoid hearing the boss’ voice?

p d q

Lets go back to our ants… The boss is not happy now that the ants have worked out how to avoid doing his orders, so he hires in another boss to help him He also invests in two Megaphones so both bosses can be heard anywhere Each ant must follow the orders of whatever boss they are standing closest to. Now the ants only way of avoiding work is to be exactly the same distance away from each boss So now where should the ants stand?

The LOCUS of a point p which is EQUIDISTANT from two other points A and B is the PERPENDICULAR BISECTOR of A and B A B p