Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.