Real-World Examples of Coordinate Plane Reflections

📚 Quick Study Guide

• 🔢 A reflection flips a point or shape over a line, called the line of reflection.
• 📈 Common lines of reflection are the x-axis ($y = 0$) and the y-axis ($x = 0$).
• 📍 Reflection over the x-axis: The x-coordinate stays the same, and the y-coordinate becomes its opposite. $(x, y) \rightarrow (x, -y)$.
• 🧭 Reflection over the y-axis: The y-coordinate stays the same, and the x-coordinate becomes its opposite. $(x, y) \rightarrow (-x, y)$.
• 📐 Reflection over the line $y=x$: The x and y coordinates are swapped. $(x, y) \rightarrow (y, x)$.
• зеркало Reflection over the line $y=-x$: The x and y coordinates are swapped and negated. $(x, y) \rightarrow (-y, -x)$.

Practice Quiz

1. Question 1: A butterfly's wing design shows symmetry across its body. If one point on the left wing is at (2, 3), where would the corresponding point be on the right wing, assuming the body is the y-axis?
   1. (-2, -3)
   2. (2, -3)
   3. (-2, 3)
   4. (3, 2)
2. Question 2: Imagine a pool table. A ball is at position (4, -1). If you want to hit the ball so it reflects off the x-axis, what would be the reflected position?
   1. (-4, -1)
   2. (4, 1)
   3. (-4, 1)
   4. (1, 4)
3. Question 3: A symmetrical building has its entrance at (-5, 2). If the building is symmetrical about the y-axis, where is the corresponding point on the other side?
   1. (5, -2)
   2. (-5, -2)
   3. (5, 2)
   4. (2, -5)
4. Question 4: A dance routine involves a reflection across an imaginary line. A dancer starts at (1, -4). After reflecting across the x-axis, where is the dancer?
   1. (-1, -4)
   2. (1, 4)
   3. (-1, 4)
   4. (4, 1)
5. Question 5: A mirror image of a point is at (-3, -5). If the mirror is on the y-axis, what were the original coordinates of the point?
   1. (3, 5)
   2. (-3, 5)
   3. (3, -5)
   4. (-5, -3)
6. Question 6: In a video game, a character at (6, 0) needs to be mirrored across the y-axis to reach a switch. What will the character's new coordinates be?
   1. (0, 6)
   2. (-6, 0)
   3. (6, 0)
   4. (0, -6)
7. Question 7: A logo design has a point at (-2, -1). To create symmetry across the x-axis, what should the reflected point be?
   1. (2, -1)
   2. (-2, 1)
   3. (2, 1)
   4. (-1, -2)