What is the algebraic rule for a figure that is rotated 270° clockwise about the origin?

Answer: (x, y) → (y, -x)

Algebraic Rules for Rotations

The algebraic rule for a figure rotated 270° clockwise about the origin is (x, y) → (y, -x). This transformation involves switching the x and y coordinates and then changing the sign of the new x-coordinate. Understanding transformations such as rotations is crucial in coordinate geometry and algebra. These concepts are widely used in fields like computer graphics, engineering design, and robotics. Grasping how to apply algebraic rules for geometric transformations enables students and professionals to visualize and manipulate objects in a spatial context.

FAQ on Geometric Transformations

What is the rule for a 180° rotation about the origin?

(x, y) → (-x, -y)

What is the rule for a 90° counterclockwise rotation?

(x, y) → (-y, x)

What is the algebraic rule for reflecting over the y-axis?

(x, y) → (-x, y)

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