Test questions on reflections over y=x and y=-x with answers

📚 Quick Study Guide

• 🔢 Reflection over y = x: To reflect a point $(x, y)$ over the line $y = x$, simply swap the x and y coordinates. The new point becomes $(y, x)$.
• 🔄 Example: If you reflect the point $(3, 2)$ over the line $y = x$, it becomes $(2, 3)$.
• ➖ Reflection over y = -x: To reflect a point $(x, y)$ over the line $y = -x$, swap the x and y coordinates and negate both. The new point becomes $(-y, -x)$.
• 💡 Example: If you reflect the point $(3, 2)$ over the line $y = -x$, it becomes $(-2, -3)$.
• 📐 General Rule: Remember to apply the transformation to each point of a shape when reflecting it.

Practice Quiz

1. What is the reflection of the point $(5, -2)$ over the line $y = x$?
   1. $(-5, 2)$
   2. $(-2, 5)$
   3. $(-5, -2)$
   4. $(-2, 5)$
2. What is the reflection of the point $(-1, 4)$ over the line $y = -x$?
   1. $(4, -1)$
   2. $(-4, 1)$
   3. $(1, -4)$
   4. $(-1, 4)$
3. The point $(7, 3)$ is reflected over the line $y = x$. What are the coordinates of the reflected point?
   1. $(-7, -3)$
   2. $(3, 7)$
   3. $(-3, -7)$
   4. $(7, 3)$
4. What is the reflection of the point $(-6, -8)$ over the line $y = -x$?
   1. $(6, 8)$
   2. $(8, 6)$
   3. $(-8, -6)$
   4. $(8, -6)$
5. A triangle has vertices at $(1, 1)$, $(2, 4)$, and $(5, 1)$. If the triangle is reflected over the line $y = x$, what are the coordinates of the reflected vertices?
   1. $(1, 1)$, $(4, 2)$, $(1, 5)$
   2. $(-1, -1)$, $(-2, -4)$, $(-5, -1)$
   3. $(1, 1)$, $(-4, -2)$, $(1, 5)$
   4. $(-1, -1)$, $(4, 2)$, $(-1, -5)$
6. What is the reflection of the point $(0, -5)$ over the line $y = -x$?
   1. $(5, 0)$
   2. $(-5, 0)$
   3. $(0, 5)$
   4. $(0, -5)$
7. The point $(-2, 2)$ is reflected over the line $y = x$, and then the resulting point is reflected over the line $y = -x$. What are the final coordinates?
   1. $(-2, 2)$
   2. $(2, -2)$
   3. $(2, 2)$
   4. $(-2, -2)$