When two or more transformations are combined we call it a composite transformation. Where t x stands for the effective, or final translation amount in x, and t y is the effective translation amount in y.
COMPOSITION OF TRANSFORMATIONS PLUS
But in either case, we can write the results of combining scaling and translation in the form x two equals s times x zero plus t x, and y two equals s times y zero plus t y. Clearly the blue equations aren't the same as the red equations. So algebraically, x two equals x one plus five, which equals four times x zero plus five and y two equals y one plus three which equals four times y zero plus three. X one equals four times x 0, and y one equals four times y zero. For comparison, let's do the operations in the opposite order. However, the effective translation amount is 20 and x and 12 and y. So the effective scale factor is still four. Y two is equal to four times y zero plus three which equals four times y zero plus 12. X two equals four times x zero plus five which equals four times x zero plus four times five, which equals four times x zero plus 20. Substitute our expressions for x one and y one. Scaling says, x two equals four times x one, and y two equals four times y one. Where does x one y one go? Let's call the point it goes to, x two y two. Now, suppose we scale about the origin by a factor of four. That point goes to a point, x one, y one, given by, x one equals x zero plus five, y one equals y zero plus three. Pick a point, x zero y zero, in the image we're translating.
Suppose we translate by an amount of five and x and three and y. Let's see if we can get a better understanding of what's going on using some algebra.
Isometry: Another word for rigid transformation, a transformation that does not change the shape or size of a figure. Rigid: A transformation that preserves size and shape. (crunch) Earlier, we saw that translation and scaling don't commute. Transformation: An operation that moves, flips, or changes a figure to create a new figure. Did you get final approval from the director? Congratulations.
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