Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine which point maps onto itself after a reflection across the line [tex]\( y = -x \)[/tex], we need to understand how reflections across this line work. The reflection of a point [tex]\((a, b)\)[/tex] across the line [tex]\( y = -x \)[/tex] transforms the point into [tex]\((-b, -a)\)[/tex].
A point [tex]\((a, b)\)[/tex] will map onto itself if and only if [tex]\((a, b) = (-b, -a)\)[/tex]. This relationship holds true if [tex]\( a = -b \)[/tex] and [tex]\( b = -a \)[/tex].
Let's verify each given point to see if it maps onto itself:
1. Point (-4, -4)
- Reflecting [tex]\((-4, -4)\)[/tex]: It becomes [tex]\((4, 4)\)[/tex]
- Clearly, [tex]\((-4, -4) \ne (4, 4)\)[/tex], so this point does not map onto itself.
2. Point (-4, 0)
- Reflecting [tex]\((-4, 0)\)[/tex]: It becomes [tex]\((0, 4)\)[/tex]
- [tex]\((-4, 0) \ne (0, 4)\)[/tex], so this point does not map onto itself.
3. Point (0, -4)
- Reflecting [tex]\((0, -4)\)[/tex]: It becomes [tex]\((4, 0)\)[/tex]
- [tex]\((0, -4) \ne (4, 0)\)[/tex], so this point does not map onto itself.
4. Point (4, -4)
- Reflecting [tex]\((4, -4)\)[/tex]: It becomes [tex]\((4, -4)\)[/tex]
- [tex]\((4, -4) = (4, -4)\)[/tex], meaning this point maps onto itself.
Therefore, the point [tex]\((4, -4)\)[/tex] maps onto itself after a reflection across the line [tex]\( y = -x \)[/tex].
So, the correct answer is:
(4, -4).
A point [tex]\((a, b)\)[/tex] will map onto itself if and only if [tex]\((a, b) = (-b, -a)\)[/tex]. This relationship holds true if [tex]\( a = -b \)[/tex] and [tex]\( b = -a \)[/tex].
Let's verify each given point to see if it maps onto itself:
1. Point (-4, -4)
- Reflecting [tex]\((-4, -4)\)[/tex]: It becomes [tex]\((4, 4)\)[/tex]
- Clearly, [tex]\((-4, -4) \ne (4, 4)\)[/tex], so this point does not map onto itself.
2. Point (-4, 0)
- Reflecting [tex]\((-4, 0)\)[/tex]: It becomes [tex]\((0, 4)\)[/tex]
- [tex]\((-4, 0) \ne (0, 4)\)[/tex], so this point does not map onto itself.
3. Point (0, -4)
- Reflecting [tex]\((0, -4)\)[/tex]: It becomes [tex]\((4, 0)\)[/tex]
- [tex]\((0, -4) \ne (4, 0)\)[/tex], so this point does not map onto itself.
4. Point (4, -4)
- Reflecting [tex]\((4, -4)\)[/tex]: It becomes [tex]\((4, -4)\)[/tex]
- [tex]\((4, -4) = (4, -4)\)[/tex], meaning this point maps onto itself.
Therefore, the point [tex]\((4, -4)\)[/tex] maps onto itself after a reflection across the line [tex]\( y = -x \)[/tex].
So, the correct answer is:
(4, -4).
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.