Loci

An army of ants work very hard all day An army of ants work very hard all day long.long.

They do everything their boss tells them, They do everything their boss tells them, all the time.all the time.

Every now and then he barks a random Every now and then he barks a random order at them just because he can.order at them just because he can.

If the ants hear the boss’ order, they must If the ants hear the boss’ order, they must obeyobey

The boss’ voice travels exactly The boss’ voice travels exactly 1metre1metre from where he standsfrom where he stands

Where are the ants safe to stand to avoid Where are the ants safe to stand to avoid hearing the boss’ voice?hearing the boss’ voice?

A story about Ants…

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The boss is not happy now that the ants The boss is not happy now that the ants have worked out how to avoid doing his have worked out how to avoid doing his orders, so he hires in another boss to help orders, so he hires in another boss to help himhim

He also invests in two Megaphones so both He also invests in two Megaphones so both bosses can be heard anywhere bosses can be heard anywhere

Each ant must follow the orders of Each ant must follow the orders of whatever boss they are standing closest whatever boss they are standing closest to.to.

Now the ants only way of avoiding work is Now the ants only way of avoiding work is to be exactly the same distance away from to be exactly the same distance away from each bosseach boss

So now where should the ants stand?So now where should the ants stand?

Lets go back to our ants…

The LOCUS of a point The LOCUS of a point p which is p which is

EQUIDISTANT from EQUIDISTANT from two other points A and two other points A and

B is the B is the PERPENDICULAR PERPENDICULAR

BISECTOR of A and BBISECTOR of A and B

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AA BB