The way that I remember it is that 90 degrees and 270 degrees are basically the opposite of each other. So, (-b, a) is for 90 degrees and (b, -a) is for 270. 180 degrees and 360 degrees are also opposites of each other. 360 degrees doesn't change since it is a full rotation or a full circle. Also this is for a counterclockwise rotation. If you want to do a clockwise rotation follow these formulas: 90 = (b, -a) 180 = (-a, -b) 270 = (-b, a) 360 = (a, b). I'm sorry about the confusion with my original message above. The "formula" for a rotation depends on the direction of the rotation. Here's something that helps me visualize it: Put another paper on top of it (I like to imagine this one as being something like a transparent sheet protector, and I draw on it using a dry-erase marker) and trace the point/shape. Now place your finger on the rotation point. The shape is being rotated! But how do we do this for a specific angle? With your finger firmly on that point, rotate the paper on top. Well, let's say the shape is a triangle with vertices A, B, and C, and we want to rotate it 90 degrees. The point at which we do the rotation, we'll call point P. The rotated triangle will be called triangle A'B'C'. As per the definition of rotation, the angles APA', BPB', and CPC', or the angle from a vertex to the point of rotation (where your finger is) to the transformed vertex, should be equal to 90 degrees. If you want, you can connect each vertex and rotated vertex to the origin to see if the angle is indeed 90 degrees. I hope this gives you more of an intuitive sense. We're told that triangle PIN is rotated negative 270ĭegrees about the origin. So this is the triangle PINĪnd we're gonna rotate it negative 270 degrees about the origin. The direction of rotationīy a positive angle is counter-clockwise. So positive is counter-clockwise, which is a standard convention, and this is negative, so a negative degree would be clockwise. rules for geometric rotations Learn with flashcards, games, and more for free. a 180 clockwise rotation about the origin. A 180 counter clockwise rotation about the origin is the same as. So what we want to do is think about, well look, if we rotate And this tool, I can put points in, or I could delete points. a 90 clockwise rotation about the origin. The points of this triangle around the origin by negative 270 degrees, where is it gonna put these points? And to help us think about that, I have copied and pasted So actually let me go over here so I can actually draw on it. So let's just first thinkĪbout what a negative 270 degree rotation actually is. If you were to start right over here and you were to rotate around So if I were to start, if I were to, let me draw some coordinate axes here.
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