Examples of Reflections in Daily Life

📚 Quick Study Guide

• 🔍 A reflection in mathematics is a transformation that flips a figure over a line, called the line of reflection.
• 📐 The reflected image is the same distance from the line of reflection as the original figure.
• ↔️ Reflections preserve size and shape, meaning the original figure and its reflection are congruent.
• 🔢 In a coordinate plane, reflecting a point $(x, y)$ over the x-axis results in the point $(x, -y)$.
• 🌌 Reflecting a point $(x, y)$ over the y-axis results in the point $(-x, y)$.
• 🧮 Reflecting a point $(x, y)$ over the line $y = x$ results in the point $(y, x)$.
• 💡 Understanding reflections helps in various fields like computer graphics, physics, and art.

Practice Quiz

1. Which of the following is the best example of a reflection in daily life?
   1. A shadow cast by a tree.
   2. The image of a building in a still lake.
   3. A car driving down a road.
   4. The changing phases of the moon.
2. If a point (3, 5) is reflected over the x-axis, what are the coordinates of the reflected point?
   1. (-3, 5)
   2. (3, -5)
   3. (-3, -5)
   4. (5, 3)
3. Which transformation is NOT a reflection?
   1. Flipping an image horizontally.
   2. Rotating a figure 90 degrees.
   3. Mirroring an object across a line.
   4. Creating a symmetrical pattern.
4. A butterfly's wings often display symmetry. This is an example of:
   1. Translation
   2. Reflection
   3. Rotation
   4. Dilation
5. If a point (2, -4) is reflected over the y-axis, what are the coordinates of the reflected point?
   1. (2, 4)
   2. (-2, -4)
   3. (-2, 4)
   4. (-4, 2)
6. Consider the word "MOM". Which of the following mathematical transformations makes it read the same way?
   1. Translation
   2. Rotation
   3. Reflection
   4. Dilation
7. If a point (1, 2) is reflected over the line $y = x$, what are the coordinates of the reflected point?
   1. (-1, 2)
   2. (2, 1)
   3. (-1, -2)
   4. (1, -2)