Transformation Martices - IGCSE

[acash09]

Hello everyone!
Hey i would like to ask ya ppl whether u have th transformation matrices for maths IGCSE?

E.G. for stretch: (in the attachments)

K is the scale factor and y axis as the invariant line

could i also have the one for shear ( x and y invar.) , rotation, and any others i didn't mention.

Thanks in advance!
Mohamed

[Kim]

hey
i used to have a wksht wid all of them
ill c if i can find it then ill send it to ya!
hopefully i have it sumwhere

[Ghost Of Highbury]

reflection in ml y=x it's (0 1)
                                (1 0)

2. refelction in ml y=-x itz (0 -1)
                                    (-1 0)

3. refelction in x-axis itz (1 0)
                                 (0 -1)

4. reflection in y-axis itz (-1 0)
                                  (0  1)

Rotation

1. rotation +90 degrees(anticlockwise) around centre(0,0)  itz (0 -1)
                                                                                    (1  0)

2. rotation -90 degrees(clockwise) around centre (0,0)  itz (0  1)
                                                                               (-1 0)

3. rotation 180 degrees around centre (0,0)  itz (-1 0)
                                                                 (0 -1)

Enlargement

1. centre (0,0) wer k=scale factor, itz (k 0)
                                                    (0 k)

Shear

1. x invariant with x-axis wer k=scale factor (1 k)
                                                            (0 1)

2. y invariant with y-axis wer k=scale factor (1 0)
                                                            (k 1)

Stretch

1. x invariant with y-axis wer k=scale factor (1 0)
                                                            (0 k)

2. y invariant with x-axis wer k=scale factor (k 0)
                                                            (0 1)

[Kim]

sorry to say cudnt find it
but u got ur answer so enjoy

[princess12]

CAN ANY ONE EXPLAIN ME TRANSLATION,TRANSFORMATION
URGENTLY PLEASE     

[the_grim_reaper]

Just one question. Does anyone know why the transformation of U to X in Nov 2009 Paper 4 IGCSE has a shear factor of -1???

[Ghost Of Highbury]

 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

[AshWINNER]

i just have a doubt in determining the invariant line

So if i am correct, if a shear leaves a line x=a invariant, so invariant line is y axis rite?

And in stretch, the axis parallel to the two points which do not change is the invariant line right

Please illustrate ne probs in my concepts

And 1 more doubt

Shear factor=Distance moved due to shear/Perp dist from inv line

If distance/displacement due to shear is towards negative ,then will the shear factor be negative
If that is true, then that explains the shear factor of -1 in nov 2009 paper

[Arthur Bon Zavi]

i just have a doubt in determining the invariant line

So if i am correct, if a shear leaves a line x=a invariant, so invariant line is y axis rite?

And in stretch, the axis parallel to the two points which do not change is the invariant line right

Please illustrate ne probs in my concepts

And 1 more doubt

Shear factor=Distance moved due to shear/Perp dist from inv line

If distance/displacement due to shear is towards negative ,then will the shear factor be negative
If that is true, then that explains the shear factor of -1 in nov 2009 paper

nov 2009 which paper 1 , 2 , 4??

[cooldude]

nov 2009 which paper 1 , 2 , 4??

42

[Arthur Bon Zavi]

42

right!!

[Heart Hacker]

Its not been 2 months and i forgot how to do it 

[SauD~]

Half Chapter In skool done not till matrices only reflection

[HUSH1994]

what is the translation's matrix,and how to determine the number of coloums and rows in a matrix after multiplying

[Vin]

what is the translation's matrix,and how to determine the number of coloums and rows in a matrix after multiplying

Translation matrix depends on the object which has moved.

[Attachment] I've tried my level best to keep is as simple as possible. Scale => 1 cm = 1 unit

The black solid triangle is the object. Red triangle is the image i.e object after moving a certain distance.

In translation, the object has the same size as the image.

1. Notice the object has moved 5 blocks to the right and 10 blocks upwards. As the scale is 1 cm = 1 unit therefore we can assume x= 5 and y = 10 Notice both are positive as they are moving along the axis.



2. The object has moved 6 blocks to the right and 10 blocks downwards. Therefore the object moves along the x axis but moves against the y axis, so x = 6 and y = -10



3. The object moves 9 blocks to the left and 5 blocks upwards, along the y axis and against the x axis. y = 5 and x = -9



4. Object moves 7 blocks downwards and 8 blocks left. Against x and y axis, x = -8 and y = -7.