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# 6. Composite transformations

We demonstrate, using algebra, why the order of two transformations - like scaling and translating - results in different outcomes. A combination of two or more transformations is called a composite transformation.

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• What is X0 and Y0? "Pick a point" as any point on the image? Because the white arrow is pointing at (0,0). I find it little bit confusing.

And when you scale about the origin by factor 4 in first case, where is the origin when it's scaled? is it (0,0) or (5,3)?
If the origin stays at (0,0) that means the translation didn't affect the origin of the object? When an object moves, its origin doesn't move with it ?

Thank you
• It wasn't explained explicitly so I can see why you're confused, but essentially you need to know that X and Y are a set of points that make up the image. The subscript 0 just means that this is where the points are initially.

If for example we had a square instead of a ball then you could say it consists of four points, and if the square had sides of length one, these points would be S = {(0, 0), (1, 0), (0, 1), (1, 1)}. So anytime we apply an operation to this square we must apply it to each point that makes up the square. To scale the square up by a factor of two, multiply each value by two: S = {(0, 0), (2, 0), (0, 2), (2, 2)}, etc.
• What is x and what is y?
(1 vote)
• the first class explains it in a very simple way
• Why are we able to change an equation by putting it in a different order, but the outcome is completely different? I know it works for subtraction and division, but I don't understand it for transformation.
• If we translate then scale from the origin, the distance from the origin is increased, so all the points move farther, but only scale it like normal!
• what happens if you dialate on an x or y axix
• You can't dialate using a line, as the definition of dilation states!
• Is there any way to make these non commutative operations, commutative?
Also, wouldn't it be better to make the lower left point of the image the rotation point?
• if you scale from the origin of the object rather than the origin of the grid, then scaling and translation operations become commutative.