Opposite Corners Grid Coursework GCSE

Hey, I really need some help with the Maths 'Opposite Corners' grid coursework, and I'm going out to the lostprophets concert tonight, and I really want to get it done before I go.

Well, the coursework is the one where there is a 10 x 10 grid, with a box drawn on it, and you have to find the different between the (top left corner x bottom right corner) and the (top right corner x bottom left corner).

I have handed this to my old maths teacher once, and he took aaaaaaaages to mark them, and has now left :frown:

Can anyone help me get the formulas for:
1. the square on a 10x10 grid
2. the rectangle on a 10x10 grid
and from there I'll be able to work out the rest.

Thanks guys, I hope you guys can help, 'cause I am bummed right now. The thing is I expanded the brackets of the formulas for (top left corner x bottom right corner) and (top right corner x bottom left corner) and found the difference, but I expanded wrong, yet I still got a formula that worked like a beast, like, everytime, but now I've redone it, it doesn't work! This sucks!

:confused:

PLEASE HELP! :confused:

I've got "For any square on the 10 x 10 grid, we would have to make a formula for an ‘n x n’ square. If ‘n’ is the number of squares across the square, the formula should be the difference between

(x+n-1)(x+10n-10)
and
x(x+10n-10+n-1)

These two equations with expanded brackets look like this:

x²+11nx-11x+10n²-20n+10
And
x²+11nx-11x

Making the clear difference between them, 10n²-20n+10, which can be simplified to 10n(n-2)+10"

But this formula, when used on 34x48 and 44x38 gets: 90, when it should clearly be 40!

Reply 1

Jonny W

But this formula, when used on 34x48 and 44x38 gets: 90, when it should clearly be 40!
That's a rectangle:

34 34 36 37 38
44 44 46 47 48

You said your formula was for squares, so let's test it out on one.

34 34 36 37 38
44 44 46 47 48
54 54 56 57 58
64 64 66 67 68
74 74 76 77 78

The answer is 38*74 - 34*78 = 160.

Your formula gives 10*5(5 - 2)+10 = 10*15 + 10 = 160. Success!

You can simplify the formula even more:

10n(n - 2)+10
= 10[n(n - 2) + 1]
= 10[n^2 - 2n + 1]
= 10(n - 1)^2

--

The method that you used for squares can be extended to rectangles. Suppose we have an n x m rectangle (n units wide, m units tall).

We want the difference between

(x + n - 1)(x + 10m - 10)
and
x (x + 10m - 10 + n - 1)

That simplifies to 10(n - 1)(m - 1).

We can test the formula against this 5 x 4 rectangle

34 34 36 37 38
44 44 46 47 48
54 54 56 57 58
64 64 66 67 68

The answer is 38*64 - 34*68 = 120.

The formula gives 10*4*3 = 120.

Reply 2

greenjm90

Cool, i understand the formula that you got for the sqaures. But i'm a bit puzzled and can't seem to adapt that to get a formula for rectangles.

Has anyone got any insite into how to do that? If you do please please tell me asap , and try to explain how you got there briefly.

Thanks alot
I know somebody out there can do it!