Write a rule to describe each of the following transformations

General
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write a rule to describe each of the following transformations

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Write a rule to describe each of the following transformations

Answer:
To describe transformations in geometry, you need to specify how points on a shape are moved to new positions. Here, we’ll cover three types of transformations: translations, rotations, and reflections. Below are rules to describe these transformations:

  1. Translation:
    A translation moves every point of a shape a constant distance in a specified direction. If you translate a point (x, y) by (a, b), the rule is:

    (x, y) \rightarrow (x + a, y + b)

    Example: Translate a shape 5 units to the right and 3 units up.

    (x, y) \rightarrow (x + 5, y + 3)

  2. Rotation:
    A rotation turns a shape around a fixed point by a certain angle. If you rotate a point (x, y) around the origin by \theta degrees counterclockwise, the rule is:

    (x, y) \rightarrow (x\cos\theta - y\sin\theta, x\sin\theta + y\cos\theta)

    Example: Rotate a shape 90^\circ counterclockwise about the origin.

    (x, y) \rightarrow (-y, x)

  3. Reflection:
    A reflection flips a shape over a specified line. If you reflect a point (x, y) over the x-axis, the rule is:

    (x, y) \rightarrow (x, -y)

    Example: Reflect a shape over the y-axis.

    (x, y) \rightarrow (-x, y)

For specific transformations provided in your examples, use the above rules and plug in the given values to describe each transformation accurately. If you need more detailed examples or have a specific transformation in mind, please let me know!

Final Answer:

  1. Translation Rule: (x, y) \rightarrow (x + a, y + b)
  2. Rotation Rule: (x, y) \rightarrow (x\cos\theta - y\sin\theta, x\sin\theta + y\cos\theta)
  3. Reflection Rule: (x, y) \rightarrow (x, -y) or (x, y) \rightarrow (-x, y), depending on the axis of reflection.