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Translations Of The T-Shape.

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Introduction

Flynn Murphy                08/05/07

Translations Of The T-Shape

For this part of the maths coursework, I will be looking at translations of the T-Shape and how the formula would change if the T-Shape was moved by a vector of         which basically means that if I move the T-Shape across one space then it is called moving it by a vector of ‘a’ and if I move the T-Shape down one space then it is called moving it by a vector of ‘b’. So, in summary, across = vector of ‘a’, and up or down = vector of ‘b’. image00.png

So now hopefully you know what a vector is, and you will be able to understand the rest of this part of my coursework (because I don’t). In the previous part of my coursework I showed how the general formula worked and this will help for this part of the coursework. If you refer back to the

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Middle

t = 31 so the start of the equation will be (5 x 31) which equals 155.

g = 12 so the second part of the equation will be (7 x 12) which equals 84.

a = 2 so the third part of my equation will be (5 x 2) which equals 10.

gb = 12 x –3 so the fourth part of my equation will be 5(12 x –3) which equals

          –180.

So, now by adding all the numbers up and putting them into an equation I will be able to prove that my prediction of the T-Number is correct:

(5 x 31) + (7 x 12) + (5 x 2) + 5(12 x –3) = T-Number

155 + 84 + 10 + -180 = 69

Now just in case you have doubts in the back of your mind that I just made up that result, then below I will back up the evidence by drawing out the 12 x 12 grid and drawing on the translation of the T-Shape step-by-step. I will now also explain another aspect of translating the T-Shape; a vector is very simple and works in the much the same way as a graph.

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Conclusion

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As you can see from the grid above, the whole 12 x 12 grid is not drawn out, this is because the whole 12 x 12 grid is not needed and I will not get extra marks simply for drawing out the whole grid. As you will also see from the grid my formula has worked, as usual, and I have also proved that with any type of vector large or small, with any sized grid large or small and with any T-Number, my formula can be used to get the answer to all your questions.

        -\  /-

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