IGCSE MATHS Doubts

[Falken_07]

Hi, I'm new here and I'm taking IGCSE for maths (and other subject) this examination session (May/June 2010)

I have a question about finding 2 by 2 matrix for transformation

Though I'm already taught how to solve it, I think it is too long and is not worth the usual 2-3 mark given for it. So anyway, here is a summary on how the solution work:
Take the 2 coordinate of the object and their respective image
ie    object--> ( 1,5 )  image--> ( -5,-1 )
      object--> ( 1,2 )  image--> ( -2,-1 )
then use formula : matrix * object = image
(a  b) * ( 1 ) = ( -5)
(c  d)    ( 5 )    ( -1)

( a+5b ) = ( -5 )
( c+5d ) = ( -1 )
and do the same for the other coordinate and finally use simultaneous equation to solve a, b, c and d

As you can see, it is quite a long procedure and I'm wondering if there is any simpler method to solve the question

Thanks in advance 

[Vin]

first of all welcome to SF !! hope u hav good time here ..

and even i use tht method .. though its quite lengthy but if u have understood it .. stick to it !! this method is really good and thers no way u may go wrong ..

[Falken_07]

first of all welcome to SF !! hope u hav good time here ..

and even i use tht method .. though its quite lengthy but if u have understood it .. stick to it !! this method is really good and thers no way u may go wrong ..

ok, thank you very much for the help 

[Vin]

always feel free to ask anytime !! By the way wat other subjects do u take ??

[$H00t!N& $t@r]

actually you dont have to do the long method if you know what the tranformation is. For example, if you know that the object has been reflected and where (whether it has been reflected in the x-axis or the y-axis) you can just write the matrix for it. Or do you not know the the matrices for tranformation?? cz its really easy if you know the matrices for each of them.

[Choc.Kits]

hey guys, my method for the matrices is that i make them up on the paper. as in, i use the identity matrix, [1 0,0 1]. plot those points on the grid, so points (1,0) and (0, 1). then i use whatever transformation matrix i need on them, so e.g. if im trying ot find the matrix of reflecting on the line y=x, i actually reflect them.

then i see the new co-ordinates. so if (1,0) became (0,1) and (0,1) became (1,0) my matrix for that transformation would be [0 1, 1 0]

im not sure if u can understand by that... but yea

[Vin]

this might help ..


https://studentforums.biz/index.php/topic,5575.msg167872.html#msg167872


our friend A@di has made life easy for us .. but i cant memorise them !!

[$H00t!N& $t@r]

but i cant memorise them !!

lol i know what you mean!    But i guess it's helpful to memorise it cz you'll just be wasting time on a question worth 2 marks! but if you're fast enough then it shouldnt be a problem... as for me im quite slow.. so yea. Nyway i started learning it like a month ago so i know them all now.

[mdwael]

Hey guys im preparing for P4 maths which to come in a few days and Ive been solving p4  oct/nov and there is a question I dont quite understand and I'd really appreciate your help.
It is question 2 on page 5 (iv) part, its about transformations and tells me to describe triangle U onto triangle X and I know its shear , y axis invariant, but the shear factor is -1, not 1 as I though, can someone please describe me how to know when the shear value is negative? thanks for your help in advance

[The Golden Girl =D]

Hey guys im preparing for P4 maths which to come in a few days and Ive been solving p4  oct/nov and there is a question I dont quite understand and I'd really appreciate your help.
It is question 2 on page 5 (iv) part, its about transformations and tells me to describe triangle U onto triangle X and I know its shear , y axis invariant, but the shear factor is -1, not 1 as I though, can someone please describe me how to know when the shear value is negative? thanks for your help in advance

which year?

[Vin]

i think its oct/nov 2009 .. tht ques is still buggin me ..

[Falken_07]

always feel free to ask anytime !! By the way wat other subjects do u take ??

Well, I'm also taking biology, chemistry, physics, computer studies, economics and EFL
(I also take examination for my native language, but its already conducted last November)

And also thanks for showing the list of the matrices for the transformation, though maybe I'll just stick to the old method

[mdwael]

which year?

Yes its oct/nov 2009 sorry I forget to mention the year

[Ghost Of Highbury]

Hey guys im preparing for P4 maths which to come in a few days and Ive been solving p4  oct/nov and there is a question I dont quite understand and I'd really appreciate your help.
It is question 2 on page 5 (iv) part, its about transformations and tells me to describe triangle U onto triangle X and I know its shear , y axis invariant, but the shear factor is -1, not 1 as I though, can someone please describe me how to know when the shear value is negative? thanks for your help in advance

w09, paper 4, 2)iv

ok this negative shear factor thingy is horrible..i cant figure it out y the move upwards is considered negative.

anyhow, its always wiser to use the matrix method

take two object and correspoding image co-ordinates..

(-4,1) --> (-4,5)

(-1,1) --> (-1,2)

check the image attached

a shear transformation matrix with y-axis is invariant is = (1  0)
                                                                            (k   1)

here k = -1

[Baladya]

http://www.freeexampapers.us/IGCSE/Maths/CIE/2007%20Jun/0580_s07_qp_4.pdf

4)e)ii) I managed to do (i) but how can we do this?

Thanks