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Transformation Matrix !!!!
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it will be better to learn them specially for shear and stretch , it will save ur tym in examz 
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yeah alot of time
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its better to memorise them....
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I'm going to try and explain a much easier method which my teacher taught me. The simultaneous equations method is way too time consuming and memorisation can be very difficult.
This method is called the "unit vector" method.
Look at the sketch. "I" is the unit vector at (1,0) and "J" is the unit vector at (0,1). It is important to remember to always start with "I" and "J" at these positions.
What you have to do is imagine you are transforming "I" and "J". For example, if you were doing a rotation of 90 degrees clockwise centre (0,0), where would these points end up? "I" would be moved to the coordinate (0,-1) and "J" would be moved to the coordinate (1,0).
Now once you know the coordinates of these two points under whatever transformation you are doing, you change these coordinates to vectors e.g. (0,-1) would become a vector with 0 (x value) on top and -1 (y value) at the bottom.
Then you put these vectors side by side to get the transformation matrix. "I" always is to the left of "J" when you are writing the matrix, as shown in the picture.
That leaves us (with the rotation example) with a matrix of (0 1)
---------------------------------------------------------(-1 0)
You can replicate this method for any transformation, even shears, stretches, and enlargements if you imagine a triangle between I, J and the origin. Just sketch the diagram in the exam and imagine the transformation of "I" and "J" in your head.
I would be able to explain this much better by demonstrating it to you live, so this might be a bit difficult to grasp. If you have any questions on the steps ask them here.
This method is called the "unit vector" method.
Look at the sketch. "I" is the unit vector at (1,0) and "J" is the unit vector at (0,1). It is important to remember to always start with "I" and "J" at these positions.
What you have to do is imagine you are transforming "I" and "J". For example, if you were doing a rotation of 90 degrees clockwise centre (0,0), where would these points end up? "I" would be moved to the coordinate (0,-1) and "J" would be moved to the coordinate (1,0).
Now once you know the coordinates of these two points under whatever transformation you are doing, you change these coordinates to vectors e.g. (0,-1) would become a vector with 0 (x value) on top and -1 (y value) at the bottom.
Then you put these vectors side by side to get the transformation matrix. "I" always is to the left of "J" when you are writing the matrix, as shown in the picture.
That leaves us (with the rotation example) with a matrix of (0 1)
---------------------------------------------------------(-1 0)
You can replicate this method for any transformation, even shears, stretches, and enlargements if you imagine a triangle between I, J and the origin. Just sketch the diagram in the exam and imagine the transformation of "I" and "J" in your head.
I would be able to explain this much better by demonstrating it to you live, so this might be a bit difficult to grasp. If you have any questions on the steps ask them here.
gratedul to uburndtjamb said:I'm going to try and explain a much easier method which my teacher taught me. The simultaneous equations method is way too time consuming and memorisation can be very difficult.
This method is called the "unit vector" method.
Look at the sketch. "I" is the unit vector at (1,0) and "J" is the unit vector at (0,1). It is important to remember to always start with "I" and "J" at these positions.
What you have to do is imagine you are transforming "I" and "J". For example, if you were doing a rotation of 90 degrees clockwise centre (0,0), where would these points end up? "I" would be moved to the coordinate (0,-1) and "J" would be moved to the coordinate (1,0).
Now once you know the coordinates of these two points under whatever transformation you are doing, you change these coordinates to vectors e.g. (0,-1) would become a vector with 0 (x value) on top and -1 (y value) at the bottom.
Then you put these vectors side by side to get the transformation matrix. "I" always is to the left of "J" when you are writing the matrix, as shown in the picture.
That leaves us (with the rotation example) with a matrix of (0 1)
---------------------------------------------------------(-1 0)
You can replicate this method for any transformation, even shears, stretches, and enlargements if you imagine a triangle between I, J and the origin. Just sketch the diagram in the exam and imagine the transformation of "I" and "J" in your head.
I would be able to explain this much better by demonstrating it to you live, so this might be a bit difficult to grasp. If you have any questions on the steps ask them here.
wat a explaination
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Keeemoman said:
That pdf basically summarises my whole post