fleet - consider what happens to the unit square (
http://en.wikipedia.org/wiki/Unit_square) after the transformations have been applied. so before we apply the transformations, the unit square has dimensions 1 x 1. now we apply the following transformations to it:
1. reflection in x-axis
2. dilation by a factor of 1/4 from the y-axis
3. translation of 1 unit in the neg dir of the x-axis
4. translation of 3 units in the pos dir of the y-axis
now what does the unit square become? well consider first the LINEAR transformations, that is all types of transformations excluding translation. so once you reflect the unit square in the x-axis and dilate it by a factor of 1/4 from the y-axis, it becomes a quadrilateral with 'dimensions' 1/4 * -1 (horizontal length * vertical height). so what are the x and y intercepts? the x intercept is (1/4,0) and the y-intercept is (0, -1). now express this in the form of a matrix:
[1/4,0;0,-1] --> notice that the coordinates of the x-intercept correspond to the entries in the first COLUMN (not row) and those of the y-intercept correspond to the entires in the second COLUMN.
premultiply the matrix [x;y] by this matrix. then add the transformation matrix, which is in this case [-1;3]
so the answer is:
[1/4,0;0,-1][x;y] + [-1;3]
hope this makes sense.
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