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# FP1 - area of quadrilateral watch

1. Hi

Question: The unit square OABC is mapped to OA'B'C' by the transformation matrix

big bracket 4 3 close big bracket
5 4

Find the co-ordinates and show that the area of the shape has not been changed by the transformation

Answer: I have found the co-ordinates to be 0(0,0), A'(4,5), B'(7,9) and C'(3,4)

the area of the unit square OABC is one but i can't for the life of me find the area of 0A'B'C'.

the formulas I have come up with google for figuring the area are only confusing me. Please point me to the Right direction.

Thanks so much
2. Can you sketch it and put two triangles and a rectangle above and the same below?
3. sketching is the way forward. Then as rnd said split it down to smaller chunks from which you can work out the whole area.
4. Since it doesn't say "hence", you could always calc. the determinant of the matrix. (Not what you're supposed to do, I'm sure).
5. (Original post by DFranklin)
Since it doesn't say "hence", you could always calc. the determinant of the matrix. (Not what you're supposed to do, I'm sure).
I can't see why it wouldn't be what you're supposed to do; it was pretty much what I had to do in my FP1 syllabus. I suppose the wording is geared towards doing it geometrically though *shrug*.

Basically, if you apply the matrix to a quadrilateral with area , then the area of the new quadrilateral is .

EDIT: That doesn't just apply to quadrilaterals; it's a scale factor, so it applies to the area of whatever shape you apply it to.
6. sorted!
7. (Original post by nuodai)
I can't see why it wouldn't be what you're supposed to do

EDIT: That doesn't just apply to quadrilaterals; it's a scale factor, so it applies to lengths and volumes of whatever shape you apply it to.

I'd bet that pepsigirl's book looks at that fact about determinants next.

Not sure about that length comment...
8. As you surmise, length is wrong.

E.g. M : (x,y) -> (x, y+x) (so M is a shear). M has det 1 and preserves area, but M(0,1) = (1,1) so doesn't preserve length.
9. (Original post by rnd)
I'd bet that pepsigirl's book looks at that fact about determinants next.

Not sure about that length comment...
I can doo maffs, me!

Consider it edited.

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