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For every point A = (x,y) in your figure, a 180 degree counterclockwise rotation about the origin will result in a point A' = (x', y') where:
x' = x * cos(180) - y * sin(180)
y' = x * sin(180) + y * cos(180)
Happy-fun time fact: This is equivalent to using a rotation matrix from Linear Algebra!
Because a rotation is an isometry, you only have to rotate each vertex of a polygon, and then connect the respective rotated vertices to get the rotated polygon.
You can rotate a closed curve as well, but you must figure out a way to rotate the infinite number of points in the curve. We are able to do this with straight lines above due to the property of isometries, which preserves distances between points.
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How many degrees has triangle ABC been rotated counterclockwise about the origin?
180 degrees.
How do you rotate a figure 270 degrees clockwise around the origin?
Move it 3 times* * * * *or once in the anti-clockwise direction.
How do you rotate a figure 270 degrees clockwise about origin?
You dont, its just 90 degrees 3 times..
How do you rotate a figure 180 degrees clockwise about origin?
To rotate a figure 180 degrees clockwise about the origin you need to take all of the coordinates of the figure and change the sign of the x-coordinates to the opposite sign(positive to negative or negative to positive). You then do the same with the y-coordinates and plot the resulting coordinates to get your rotated figure.
What is the image of (1 -6) for a 90 and deg counterclockwise rotation about the origin?
It is (-1, 6).
