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R(90°)

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Honors Geometry

Definition

The term r(90°) refers to a rotation of 90 degrees about a specified point in a coordinate plane. This transformation involves turning a figure or point counterclockwise by 90 degrees around a center of rotation, which results in a new position for each point of the figure. Understanding r(90°) is crucial as it relates closely to other transformations like translations and reflections, which are fundamental concepts in geometry.

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5 Must Know Facts For Your Next Test

  1. When rotating a point (x, y) by r(90°) around the origin, the new coordinates become (-y, x).
  2. Rotating a figure by r(90°) preserves the size and shape of the figure, making it an isometric transformation.
  3. In terms of symmetry, a 90-degree rotation creates rotational symmetry for figures that are arranged in specific patterns.
  4. The direction of rotation for r(90°) is always counterclockwise unless otherwise specified.
  5. If you rotate multiple points or figures using r(90°), each point moves in a consistent manner relative to the center of rotation.

Review Questions

  • How does the transformation r(90°) change the coordinates of a point in the coordinate plane?
    • The transformation r(90°) rotates a point counterclockwise by 90 degrees around the origin. For any point with coordinates (x, y), after applying r(90°), the new coordinates will be (-y, x). This means that the x-coordinate becomes the negative y-coordinate, and the y-coordinate takes the original x-coordinate's place, effectively turning the point around the center of rotation.
  • Compare r(90°) with reflection transformations. How do their effects on points differ?
    • While both r(90°) and reflections are types of transformations that reposition points, their methods and outcomes differ significantly. A reflection flips a point over a specific line, such as the x-axis or y-axis, maintaining its distance from that line. In contrast, r(90°) rotates points around a center without mirroring them across an axis. The result is that points move to entirely different locations rather than simply being flipped over an axis.
  • Evaluate how understanding r(90°) can assist in solving more complex geometric problems involving multiple transformations.
    • Understanding r(90°) helps build a foundation for solving complex geometric problems by allowing students to visualize and execute multiple transformations in sequence. For example, if you need to rotate and then reflect a shape, knowing how each transformation affects the coordinates individually enables you to track changes accurately. This skill not only aids in calculations but also enhances spatial reasoning, enabling better problem-solving strategies in geometric scenarios involving various transformations.

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