Hi
These four points A(3,1), B(5/2,2), C(9/2,3), D(5,2)
Is turned 90 degrees clockwise around the center of the figure.
I'm supposed to write a transformation that does this.
I get the following:
![(x,y) \rightarrow \left[ \begin{array}{cc} -cos( 2 \theta ) & sin(2 \theta) \\ sin(2 \theta) & cos(2 \theta) \end{array} \right] \left[ \begin{array}{c} x \\ y \end{array} \right]](http://latex.codecogs.com/png.latex?(x,y) \rightarrow \left[ \begin{array}{cc} -cos( 2 \theta ) & sin(2 \theta) \\ sin(2 \theta) & cos(2 \theta) \end{array} \right] \left[ \begin{array}{c} x \\ y \end{array} \right])
My teacher is says this is wrong cause any transformations that isn't rotated around (0,0) is not a linear transformation.
If thats true what should the transformation then look like ???
/Fred
Let's say a rotation of the desired form abou the origin is of the formOriginally Posted by Mathman24
where A is a matrix and x and y are 2-vectors. You'll have to determine the matrix A - your solution isn't correct since it doesn't pay attention to the 90 degrees. Such a rotation is linear.
Suppose now you want to rotate about a different point, say. Set
. This is the displacement of the point x from
Thenis the rotated position vector, relative to the point
is the formula for the rotation about
Hi can't it be made correct if I add the distance between the original point and the center of the figure ??
/Fred
Let's say a rotation of the desired form abou the origin is of the form
Suppose now you want to rotate about a different point, say
Then
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