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

💡 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