# Hexagon, coordinates, base

#### Petrus

##### Well-known member
Consider a regular hexagon ABCDEF (in order counterclockwise). Determine the coordinates of AB, AE AND AF (->) in the base (AC, AD) (->)

AB(->)=(_____,_____)
AE(->)=(_____,_____)
AF(->)=(_____,_____)

what I mean with exemple AF(->) positive way from A to F. I have draw a it but I got problem to rewrite
I got AE=EF+FA(->) I am correct?

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#### Petrus

##### Well-known member
Re: hexagon, coordinates, base

I could uppload picture from internet but it should be insted of F it should B. In ourder counterclockwise. Well I can rewrite AE=EF+FA (->)

#### HallsofIvy

##### Well-known member
MHB Math Helper
Re: hexagon, coordinates, base

No, you have the order wrong: AE= AF+ FE.

#### Petrus

##### Well-known member
Re: hexagon, coordinates, base

No, you have the order wrong: AE= AF+ FE.
Yeah I forgot to Edit. How do I do for AF and AB? Then I got Also My base.

#### Petrus

##### Well-known member
Re: hexagon, coordinates, base

So I draw it.
We know from origo to A it is 1 and origo to D it is 1.

#### Petrus

##### Well-known member
I think I have thought wrong...
We got the base AC and AD and I put $$\displaystyle AC=(1,0)$$ and $$\displaystyle AD(0,1)$$
We know that $$\displaystyle AC=AB+BC$$ ( ->) that means $$\displaystyle AB=AC-BC <=> AB=AC-BC$$ and we know that $$\displaystyle AC=(1,0)$$ That means $$\displaystyle AB=(1,0)-BC$$ But is BC same as from A to origo?

#### Petrus

##### Well-known member
So I did wrong... After alot reading I think I got correct progress now...
We know it says regular hexagon that means from origo to any point got the lenght 1.
A circle is 360 degree and we got 8 lines. $$\displaystyle \frac{360}{8}=45$$ So we got now (look picture). we know x value is cos and y value is sin so we know
$$\displaystyle A=(1,0)$$
$$\displaystyle B=(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}})$$
$$\displaystyle C=(-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}})$$
$$\displaystyle D=(-1,0)$$
$$\displaystyle E=(-\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}})$$
$$\displaystyle F=(\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}})$$
That means
$$\displaystyle AC=(-\frac{1}{\sqrt{2}}-1,\frac{1}{\sqrt{2}})$$
$$\displaystyle AD=(-2,0)$$
----
$$\displaystyle AB=(\frac{1}{\sqrt{2}}-1,\frac{1}{\sqrt{2}})$$
$$\displaystyle AE=(-\frac{1}{\sqrt{2}}-1,-\frac{1}{\sqrt{2}})$$
$$\displaystyle AF=(\frac{1}{\sqrt{2}}-1,-\frac{1}{\sqrt{2}})$$
So now I got all point but got problem to determine our cordinate with our base.

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