Reflections Over X and Y Axis: Definition, Rules, and Examples

📚 Quick Study Guide

• 📍 Reflection over the X-axis: The x-coordinate stays the same, and the y-coordinate changes its sign. If the point is $(x, y)$, the reflected point is $(x, -y)$.
• 📈 Reflection over the Y-axis: The y-coordinate stays the same, and the x-coordinate changes its sign. If the point is $(x, y)$, the reflected point is $(-x, y)$.
• 📐 Example: Reflecting the point $(2, 3)$ over the X-axis gives $(2, -3)$. Reflecting it over the Y-axis gives $(-2, 3)$.
• 💡 Mnemonic: X-axis reflection changes the *y*-value's sign, Y-axis reflection changes the *x*-value's sign.
• 📝 Formula:
  • Reflection over X-axis: $(x, y) \rightarrow (x, -y)$
  • Reflection over Y-axis: $(x, y) \rightarrow (-x, y)$

🧠 Practice Quiz

1. What are the coordinates of the point $(4, -2)$ after reflection over the X-axis?
   1. (A) $(-4, -2)$
   2. (B) $(4, 2)$
   3. (C) $(-4, 2)$
   4. (D) $(4, -2)$
2. What are the coordinates of the point $(-1, 5)$ after reflection over the Y-axis?
   1. (A) $(1, 5)$
   2. (B) $(-1, -5)$
   3. (C) $(1, -5)$
   4. (D) $(-1, 5)$
3. The point $(3, 7)$ is reflected over the X-axis and then over the Y-axis. What are the final coordinates?
   1. (A) $(-3, -7)$
   2. (B) $(3, -7)$
   3. (C) $(-3, 7)$
   4. (D) $(3, 7)$
4. A point is reflected over the Y-axis and its image is $(-5, 2)$. What were the original coordinates of the point?
   1. (A) $(5, -2)$
   2. (B) $(-5, -2)$
   3. (C) $(5, 2)$
   4. (D) $(-5, 2)$
5. If a point $(a, b)$ reflected over the X-axis is $(a, -b)$, which axis does not change?
   1. (A) X-axis
   2. (B) Y-axis
   3. (C) Both axes
   4. (D) Neither axis
6. The point $(-6, -4)$ is reflected over the Y-axis. What are the new coordinates?
   1. (A) $(-6, 4)$
   2. (B) $(6, -4)$
   3. (C) $(6, 4)$
   4. (D) $(-6, -4)$
7. Reflecting the point $(0, -8)$ over the X-axis results in which coordinates?
   1. (A) $(0, 8)$
   2. (B) $(0, -8)$
   3. (C) $(8, 0)$
   4. (D) $(-8, 0)$