Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To determine which reflection produces the specified endpoints, let's review various transformations:
1. Reflection across the [tex]\(x\)[/tex]-axis:
- Reflecting a point [tex]\((x, y)\)[/tex] across the [tex]\(x\)[/tex]-axis results in [tex]\((x, -y)\)[/tex].
- For [tex]\((-4, -6)\)[/tex], reflecting it across the [tex]\(x\)[/tex]-axis gives us [tex]\((-4, 6)\)[/tex].
- For [tex]\((-6, 4)\)[/tex], reflecting it across the [tex]\(x\)[/tex]-axis gives us [tex]\((-6, -4)\)[/tex].
- The endpoints after reflection are: [tex]\((-4, 6)\)[/tex] and [tex]\((-6, -4)\)[/tex].
2. Reflection across the [tex]\(y\)[/tex]-axis:
- Reflecting a point [tex]\((x, y)\)[/tex] across the [tex]\(y\)[/tex]-axis results in [tex]\((-x, y)\)[/tex].
- For [tex]\((-4, -6)\)[/tex], reflecting it across the [tex]\(y\)[/tex]-axis gives us [tex]\((4, -6)\)[/tex].
- For [tex]\((-6, 4)\)[/tex], reflecting it across the [tex]\(y\)[/tex]-axis gives us [tex]\((6, 4)\)[/tex].
- The endpoints after reflection are: [tex]\((4, -6)\)[/tex] and [tex]\((6, 4)\)[/tex].
3. Reflection across the line [tex]\(y = x\)[/tex]:
- Reflecting a point [tex]\((x, y)\)[/tex] across the line [tex]\(y = x\)[/tex] results in [tex]\((y, x)\)[/tex].
- For [tex]\((-4, -6)\)[/tex], reflecting it across the line [tex]\(y = x\)[/tex] gives us [tex]\((-6, -4)\)[/tex].
- For [tex]\((-6, 4)\)[/tex], reflecting it across the line [tex]\(y = x\)[/tex] gives us [tex]\((4, -6)\)[/tex].
- The endpoints after reflection are: [tex]\((-6, -4)\)[/tex] and [tex]\((4, -6)\)[/tex].
4. Reflection across the line [tex]\(y = -x\)[/tex]:
- Reflecting a point [tex]\((x, y)\)[/tex] across the line [tex]\(y = -x\)[/tex] results in [tex]\((-y, -x)\)[/tex].
- For [tex]\((-4, -6)\)[/tex], reflecting it across the line [tex]\(y = -x\)[/tex] gives us [tex]\((6, 4)\)[/tex].
- For [tex]\((-6, 4)\)[/tex], reflecting it across the line [tex]\(y = -x\)[/tex] gives us [tex]\((-4, -6)\)[/tex].
- The endpoints after reflection are: [tex]\((6, 4)\)[/tex] and [tex]\((-4, -6)\)[/tex].
We want the reflected line segment to have endpoints [tex]\((4, -6)\)[/tex] and [tex]\((8, 4)\)[/tex]. Let's compare this with our results:
- Reflection across the [tex]\(x\)[/tex]-axis gives endpoints [tex]\((-4, 6)\)[/tex] and [tex]\((-6, -4)\)[/tex].
- Reflection across the [tex]\(y\)[/tex]-axis gives endpoints [tex]\((4, -6)\)[/tex] and [tex]\((6, 4)\)[/tex].
- Reflection across the line [tex]\(y = x\)[/tex] gives endpoints [tex]\((-6, -4)\)[/tex] and [tex]\((4, -6)\)[/tex].
- Reflection across the line [tex]\(y = -x\)[/tex] gives endpoints [tex]\((6, 4)\)[/tex] and [tex]\((-4, -6)\)[/tex].
None of the reflections match the desired endpoints of [tex]\((4, -6)\)[/tex] and [tex]\((8, 4)\)[/tex]. Therefore, it is concluded that the specified reflection does not produce the required endpoints.
1. Reflection across the [tex]\(x\)[/tex]-axis:
- Reflecting a point [tex]\((x, y)\)[/tex] across the [tex]\(x\)[/tex]-axis results in [tex]\((x, -y)\)[/tex].
- For [tex]\((-4, -6)\)[/tex], reflecting it across the [tex]\(x\)[/tex]-axis gives us [tex]\((-4, 6)\)[/tex].
- For [tex]\((-6, 4)\)[/tex], reflecting it across the [tex]\(x\)[/tex]-axis gives us [tex]\((-6, -4)\)[/tex].
- The endpoints after reflection are: [tex]\((-4, 6)\)[/tex] and [tex]\((-6, -4)\)[/tex].
2. Reflection across the [tex]\(y\)[/tex]-axis:
- Reflecting a point [tex]\((x, y)\)[/tex] across the [tex]\(y\)[/tex]-axis results in [tex]\((-x, y)\)[/tex].
- For [tex]\((-4, -6)\)[/tex], reflecting it across the [tex]\(y\)[/tex]-axis gives us [tex]\((4, -6)\)[/tex].
- For [tex]\((-6, 4)\)[/tex], reflecting it across the [tex]\(y\)[/tex]-axis gives us [tex]\((6, 4)\)[/tex].
- The endpoints after reflection are: [tex]\((4, -6)\)[/tex] and [tex]\((6, 4)\)[/tex].
3. Reflection across the line [tex]\(y = x\)[/tex]:
- Reflecting a point [tex]\((x, y)\)[/tex] across the line [tex]\(y = x\)[/tex] results in [tex]\((y, x)\)[/tex].
- For [tex]\((-4, -6)\)[/tex], reflecting it across the line [tex]\(y = x\)[/tex] gives us [tex]\((-6, -4)\)[/tex].
- For [tex]\((-6, 4)\)[/tex], reflecting it across the line [tex]\(y = x\)[/tex] gives us [tex]\((4, -6)\)[/tex].
- The endpoints after reflection are: [tex]\((-6, -4)\)[/tex] and [tex]\((4, -6)\)[/tex].
4. Reflection across the line [tex]\(y = -x\)[/tex]:
- Reflecting a point [tex]\((x, y)\)[/tex] across the line [tex]\(y = -x\)[/tex] results in [tex]\((-y, -x)\)[/tex].
- For [tex]\((-4, -6)\)[/tex], reflecting it across the line [tex]\(y = -x\)[/tex] gives us [tex]\((6, 4)\)[/tex].
- For [tex]\((-6, 4)\)[/tex], reflecting it across the line [tex]\(y = -x\)[/tex] gives us [tex]\((-4, -6)\)[/tex].
- The endpoints after reflection are: [tex]\((6, 4)\)[/tex] and [tex]\((-4, -6)\)[/tex].
We want the reflected line segment to have endpoints [tex]\((4, -6)\)[/tex] and [tex]\((8, 4)\)[/tex]. Let's compare this with our results:
- Reflection across the [tex]\(x\)[/tex]-axis gives endpoints [tex]\((-4, 6)\)[/tex] and [tex]\((-6, -4)\)[/tex].
- Reflection across the [tex]\(y\)[/tex]-axis gives endpoints [tex]\((4, -6)\)[/tex] and [tex]\((6, 4)\)[/tex].
- Reflection across the line [tex]\(y = x\)[/tex] gives endpoints [tex]\((-6, -4)\)[/tex] and [tex]\((4, -6)\)[/tex].
- Reflection across the line [tex]\(y = -x\)[/tex] gives endpoints [tex]\((6, 4)\)[/tex] and [tex]\((-4, -6)\)[/tex].
None of the reflections match the desired endpoints of [tex]\((4, -6)\)[/tex] and [tex]\((8, 4)\)[/tex]. Therefore, it is concluded that the specified reflection does not produce the required endpoints.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.