Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Quadrilateral ABCD is transformed according to the rule [tex]\((x, y) \rightarrow (y, -x)\)[/tex]. Which is another way to state the transformation?

A. [tex]\(R_{0,90^{\circ}}\)[/tex]
B. [tex]\(R_{0,180^{\circ}}\)[/tex]
C. [tex]\(R_{0,270^{\circ}}\)[/tex]
D. [tex]\(R_{0,360^{\circ}}\)[/tex]

Sagot :

GinnyAnswer
To determine the correct way to state the transformation given by [tex]\((x, y) \rightarrow (y, -x)\)[/tex], we need to analyze the nature of the transformation.

1. The original coordinates [tex]\((x, y)\)[/tex] of a point are transformed to new coordinates [tex]\((y, -x)\)[/tex]. This type of transformation is a rotation because both coordinates change in a manner consistent with rotating around the origin.

2. Let's consider the specific effects of the transformation:
- The original x-coordinate becomes the new y-coordinate.
- The original y-coordinate changes sign and becomes the new x-coordinate, but with a negative sign.

3. To identify which rotation this corresponds to, visualize the point [tex]\((x, y)\)[/tex] on the coordinate plane:
- When we rotate a point 90 degrees counterclockwise around the origin, the new position of [tex]\((x, y)\)[/tex] would be precisely [tex]\((y, -x)\)[/tex].

4. This matches our transformation rule exactly. Therefore, the transformation [tex]\((x, y) \rightarrow (y, -x)\)[/tex] is indeed a rotation by 90 degrees counterclockwise around the origin.

Therefore, the correct way to state the transformation is [tex]\(R_{0,90^{\circ}}\)[/tex].
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.