this post was submitted on 24 Aug 2024
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The scaled down rectangle should be narrower; it's not scaled in this diagram, it's squished.
(Yes I know you can 'scale' objects on one axis but that's usually not how it's taught on an introductory level. Standard scaling assumes object similarity, which is not present in the diagram's 'scaled' rectangle.)
This is some quality pedantry.
Scaling in 2D has 2 parameters, X and Y, in the example X was at 1 while Y was below 1. You are referring to a subset of scaling transformation where X = Y and the aspect ratio is kept.
Yes, and introductory geometry courses teach students how to do uniform scaling far before they teach them axis-based because it's better illustrative of the concepts of similarity and congruence
And what about the arrow?
It's pointing down diagonally, which - at least to me (and for pretty much any GUI I can think of) - indicates, that it should be affecting both axes.
Then again, that whole illustration isn't all that great to begin with. So who knows, what that arrow is supposed to signify...
No, I wod say scaling is any diagonal matrix and thus even includes mirroring.
Cool, now explain that to a class of 7th graders for me
edit: raised grade, it may been set a low but it varies. I think most kids start to learn this stuff in/around middle school
edit 2: also mirrored objects are generally considered similar so that's fine
Ackchuawually, this example depicts a squish and a translation. A true scaling would have the scaling being done in place, resulting in an overlayed and smaller rectangle.
Damnit, I wanted to say that