Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

One vertex of a triangle is located at [tex]\((0, 5)\)[/tex] on a coordinate grid. After a transformation, the vertex is located at [tex]\((5, 0)\)[/tex].

Which transformations could have taken place? Select two options.

A. [tex]\(R_{0, 90^{\circ}}\)[/tex]

B. [tex]\(R_{0, 180^{\circ}}\)[/tex]

C. [tex]\(R_{0, 270^{\circ}}\)[/tex]

D. [tex]\(R_{0, -90^{\circ}}\)[/tex]

E. [tex]\(R_{0, -180^{\circ}}\)[/tex]

Sagot :

GinnyAnswer
Certainly! Let's determine which transformations could result in the vertex of the triangle moving from [tex]\((0,5)\)[/tex] to [tex]\((5,0)\)[/tex].

### Transformation Descriptions:
1. [tex]\(R_{0,90^{\circ}}\)[/tex]: A rotation by [tex]\(90^\circ\)[/tex] counterclockwise around the origin.
2. [tex]\(R_{0,180^{\circ}}\)[/tex]: A rotation by [tex]\(180^\circ\)[/tex] around the origin.
3. [tex]\(R_{0,270^{\circ}}\)[/tex]: A rotation by [tex]\(270^\circ\)[/tex] counterclockwise around the origin.
4. [tex]\(R_{0,-90^{\circ}}\)[/tex]: A rotation by [tex]\(90^\circ\)[/tex] clockwise around the origin.
5. [tex]\(R_{0,-180^{\circ}}\)[/tex]: A rotation by [tex]\(180^\circ\)[/tex] clockwise around the origin.

### Applying Transformations:
1. [tex]\(R_{0,90^{\circ}}\)[/tex]: Rotation by [tex]\(90^\circ\)[/tex] counterclockwise
- Starting point: [tex]\((0,5)\)[/tex]
- Transformation to: [tex]\((-5,0)\)[/tex]
- Result: [tex]\((-5,0)\)[/tex], which is not [tex]\((5,0)\)[/tex].

2. [tex]\(R_{0,180^{\circ}}\)[/tex]: Rotation by [tex]\(180^\circ\)[/tex]
- Starting point: [tex]\((0,5)\)[/tex]
- Transformation to: [tex]\((0,-5)\)[/tex]
- Result: [tex]\((0,-5)\)[/tex], which is not [tex]\((5,0)\)[/tex].

3. [tex]\(R_{0,270^{\circ}}\)[/tex]: Rotation by [tex]\(270^\circ\)[/tex] counterclockwise
- Starting point: [tex]\((0,5)\)[/tex]
- Transformation to: [tex]\((5,0)\)[/tex]
- Result: [tex]\((5,0)\)[/tex], which matches the transformed coordinates.

4. [tex]\(R_{0,-90^{\circ}}\)[/tex]: Rotation by [tex]\(90^\circ\)[/tex] clockwise
- Starting point: [tex]\((0,5)\)[/tex]
- Transformation to: [tex]\((5,0)\)[/tex]
- Result: [tex]\((5,0)\)[/tex], which matches the transformed coordinates.

5. [tex]\(R_{0,-180^{\circ}}\)[/tex]: Rotation by [tex]\(180^\circ\)[/tex] clockwise
- Starting point: [tex]\((0,5)\)[/tex]
- Transformation to: [tex]\((0,-5)\)[/tex]
- Result: [tex]\((0,-5)\)[/tex], which is not [tex]\((5,0)\)[/tex].

### Conclusion:
The valid transformations are [tex]\(R_{0,270^{\circ}}\)[/tex] and [tex]\(R_{0,-90^{\circ}}\)[/tex], as they both result in the vertex moving from [tex]\((0,5)\)[/tex] to [tex]\((5,0)\)[/tex].

Hence, the correct options are:
- [tex]\(R_{0,270^{\circ}}\)[/tex]
- [tex]\(R_{0,-90^{\circ}}\)[/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.