Answered

IDNLearn.com is your go-to resource for finding expert answers and community support. Ask anything and receive thorough, reliable answers from our community of experienced professionals.

Marissa wants to write an abbreviated set of directions for finding the coordinates of a figure reflected across the [tex]$y$[/tex]-axis. Which mapping notation is correct?

A. [tex]$(x, y) \rightarrow (-x, y)$[/tex]
B. [tex]$(x, y) \rightarrow (x, -y)$[/tex]
C. [tex]$(x, y) \rightarrow (-x, -y)$[/tex]
D. [tex]$(x, y) \rightarrow (y, x)$[/tex]

Sagot :

GinnyAnsweridn
To determine the correct mapping notation for reflecting a point [tex]\((x, y)\)[/tex] across the [tex]\(y\)[/tex]-axis, we need to understand how this transformation affects the coordinates of the point.

1. Understanding Reflections Across the [tex]\(y\)[/tex]-axis:
- When a point [tex]\((x, y)\)[/tex] is reflected across the [tex]\(y\)[/tex]-axis, its [tex]\(y\)[/tex]-coordinate remains the same while its [tex]\(x\)[/tex]-coordinate changes sign. This means the point [tex]\((x, y)\)[/tex] will move to [tex]\((-x, y)\)[/tex].

2. Analyzing Options:
- Option 1: [tex]\((x, y) \rightarrow (-x, y)\)[/tex]
- This matches our understanding of a reflection across the [tex]\(y\)[/tex]-axis. The [tex]\(x\)[/tex]-coordinate changes sign, becoming [tex]\(-x\)[/tex], while the [tex]\(y\)[/tex]-coordinate remains the same.
- Option 2: [tex]\((x, y) \rightarrow (x, -y)\)[/tex]
- This would represent a reflection across the [tex]\(x\)[/tex]-axis, not the [tex]\(y\)[/tex]-axis. Here, the [tex]\(y\)[/tex]-coordinate changes sign, becoming [tex]\(-y\)[/tex], while the [tex]\(x\)[/tex]-coordinate remains the same.
- Option 3: [tex]\((x, y) \rightarrow (-x, -y)\)[/tex]
- This would represent a rotation of 180 degrees around the origin, not a reflection across the [tex]\(y\)[/tex]-axis. Both coordinates change sign.
- Option 4: [tex]\((x, y) \rightarrow (y, x)\)[/tex]
- This would represent neither a reflection across the [tex]\(y\)[/tex]-axis nor any common reflection. It essentially swaps the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates.

3. Conclusion:
- Based on the definitions and transformations provided, the correct mapping notation for reflecting a point [tex]\((x, y)\)[/tex] across the [tex]\(y\)[/tex]-axis is the first one: [tex]\((x, y) \rightarrow (-x, y)\)[/tex].

Hence, the correct abbreviated set of directions for reflecting a point [tex]\((x, y)\)[/tex] across the [tex]\(y\)[/tex]-axis follows the notation:
[tex]\[ (x, y) \rightarrow (-x, y) \][/tex]

Therefore, Marissa should choose Option 1: [tex]\((x, y) \rightarrow (-x, y)\)[/tex].
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.