That and it looks like it is getting us right to point A. where k is the vertical shift, h is the horizontal shift, a is the vertical stretch and. Thus, we get the general formula of transformations as. Our center of rotation, this is our point P, and we're rotating by negative 90 degrees. Suppose we need to graph f (x) 2 (x-1) 2, we shift the vertex one unit to the right and stretch vertically by a factor of 2. 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. And it looks like it's the same distance from the origin. 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. See examples, video, and practice problems with step-by-step solutions. One way to think about 60 degrees, is that that's 1/3 of 180 degrees. Learn how to describe and graph rotational transformations, such as 90, 180, and 270 rotations, and how to identify rotational symmetry, order, and magnitude of rotations. So this looks like aboutĦ0 degrees right over here. Use a protractor to measure the specified angle counterclockwise. P is right over here and we're rotating by positive 60 degrees, so that means we go counterĬlockwise by 60 degrees. The amount of rotation is called the angle of rotation and it is measured in 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 If this triangle is rotated 90° counterclockwise. (-y, x) Example 1 : Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. That point P was rotated about the origin (0,0) by 60 degrees. When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure. 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). 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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