Final answer:
To rotate a shape 60 degrees counterclockwise, each point of the shape moves in the opposite direction of a clock's hands. For coordinate geometry, the new coordinates (x', y') are calculated using the formulas x' = x × cos(60°) - y × sin(60°) and y' = x × sin(60°) + y × cos(60°).
Step-by-step explanation:
Rule for Rotating a Shape 60 Degrees Counterclockwise
To rotate a shape 60 degrees counterclockwise around a point, each point of the shape must move along the arc of a circle with a radius equal to the distance from the point to the center of rotation. The direction of movement is opposite to the direction of a clock's hands. When dealing with coordinate geometry, there is a specific rule that can be applied to rotate points 60 degrees counterclockwise on a coordinate plane:
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- First, convert the angle of rotation to radians if necessary.
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- Then, for each point (x, y) on the shape, calculate the new coordinates (x', y') by applying the following transformations:
x' = x × cos(60°) - y × sin(60°)
y' = x × sin(60°) + y × cos(60°)
This results in each point moving to a new position that is 60 degrees away from its original location, following the direction of counterclockwise rotation.