![]() That and it looks like it is getting us right to point A. With a 90-degree rotation around the origin, (x,y) becomes (-y,x) Now lets consider a 180-degree rotation: We can see another predictable pattern here. Our center of rotation, this is our point P, and we're rotating by negative 90 degrees. Which point is the image of P? So once again, pause this video and try to think about it. Than 60 degree rotation, so I won't go with that one. In short, switch x and y and make x negative. ![]() ![]() And it looks like it's the same distance from the origin. 90 Degree Clockwise Rotation If a point is rotating 90 degrees clockwise about the origin our point M (x,y) becomes M (y,-x). Like 1/3 of 180 degrees, 60 degrees, it gets us to point C. So does this look like 1/3 of 180 degrees? Remember, 180 degrees wouldīe almost a full line. One way to think about 60 degrees, is that that's 1/3 of 180 degrees. So this looks like aboutĦ0 degrees right over here. Rotating a polygon clockwise 90 degrees around the origin. P is right over here and we're rotating by positive 60 degrees, so that means we go counterĬlockwise by 60 degrees. It's being rotated around the origin (0,0) by 60 degrees. Which point is the image of P? Pause this video and see That point P was rotated about the origin (0,0) by 60 degrees. A rotation by 90 is like tipping the rectangle on its side: 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 y x A A Now we see that the image of A ( 3, 4) under the rotation is A ( 4, 3). A rotation is a type of rigid transformation, which means it changes the position or orientation of an image without changing its size or shape. I included some other materials so you can also check it out. There are many different explains, but above is what I searched for and I believe should be the answer to your question. There is also a system where positive degree is clockwise and negative degree anti-clockwise, but it isn't widely used. Product of unit vector in X direction with that in the Y direction has to be the unit vector in the Z direction (coming towards us from the origin). Determining rotations Google Classroom About Transcript To see the angle of rotation, we draw lines from the center to the same point in the shape before and after the rotation. Clockwise for negative degree.įor your second question, it is mainly a conventional that mathematicians determined a long time ago for easier calculation in various aspects such as vectors.
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