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JordanOh honey, it's as simple as pie! The formula for a 180 degree counterclockwise rotation is just (-x, -y). Just flip those coordinates like you're flipping pancakes at a Sunday brunch, and you'll have yourself a perfectly rotated shape. Just remember, math is like a recipe - follow the steps and you'll end up with a delicious result!
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Why doesn't the direction of rotation clockwise and counterclockwise matter when the angle of rotation is 180?
Because 180 degrees clockwise is the same as 180 degrees counterclockwise.
What is the image of 1 -6 after a 180 degree counterclockwise rotation about the origin?
A 180° rotation is half a rotation and it doesn't matter if it is clockwise of counter clockwise. When rotating 180° about the origin, the x-coordinate and y-coordinates change sign Thus (1, -6) → (-1, 6) after rotating 180° around the origin.
What is the degree for a half of rotation?
180 degrees
What does a 540 degree look like?
360 degrees would be one full rotation. 180 degrees would be a half rotation. 360+180=540 So it would be a rotation and a half.
How do you rotate a figure 180 degrees counterclockwise around the origin?
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.
