joel838
joel838 5d ago • 0 views

25 Amazing Real-World Examples of Translations, Reflections, and Rotations

Hey there! 👋 Ever wondered where math meets the real world? Let's explore how translations, reflections, and rotations pop up everywhere! ➕
🧮 Mathematics

1 Answers

✅ Best Answer

💡 Translations, Reflections, and Rotations: Quick Study Guide

  • 📏 Translation: Moving a shape without rotating or reflecting it. Every point moves the same distance in the same direction.
  • зеркало Reflection: Flipping a shape over a line (the line of reflection). The reflected shape is a mirror image of the original.
  • 🔄 Rotation: Turning a shape around a fixed point (the center of rotation). Defined by the angle and direction of rotation.
  • 📐 Formulas:
    • Translation: $(x, y) \rightarrow (x + a, y + b)$
    • Reflection over x-axis: $(x, y) \rightarrow (x, -y)$
    • Reflection over y-axis: $(x, y) \rightarrow (-x, y)$
    • Rotation 90° counterclockwise: $(x, y) \rightarrow (-y, x)$
    • Rotation 180°: $(x, y) \rightarrow (-x, -y)$

❓ Quiz Time!

  1. A slide at a water park is an example of which transformation?
    1. Rotation
    2. Reflection
    3. Translation
    4. Dilation
  2. Looking at your reflection in a mirror demonstrates which transformation?
    1. Translation
    2. Rotation
    3. Reflection
    4. Dilation
  3. The hands of a clock moving around the clock face exemplify which transformation?
    1. Translation
    2. Rotation
    3. Reflection
    4. Dilation
  4. Which transformation is used when creating a tessellation (tiling) pattern?
    1. Translation
    2. Rotation
    3. Reflection
    4. All of the above
  5. A figure is reflected over the y-axis. If a point on the original figure is (3, 5), what are the coordinates of the corresponding point on the reflected image?
    1. (3, -5)
    2. (-3, 5)
    3. (-3, -5)
    4. (5, 3)
  6. A figure is rotated 90 degrees counterclockwise about the origin. If a point on the original figure is (2, -1), what are the coordinates of the corresponding point on the rotated image?
    1. (-1, -2)
    2. (1, 2)
    3. (-1, 2)
    4. (2, 1)
  7. A park designer wants to move a statue 10 feet east and 5 feet north. What type of transformation is this?
    1. Rotation
    2. Reflection
    3. Translation
    4. Dilation
🔑 Answer Key
  1. C
  2. C
  3. A
  4. D
  5. B
  6. B
  7. C

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