Answered

Join the IDNLearn.com community and get your questions answered by experts. Our Q&A platform offers detailed and trustworthy answers to ensure you have the information you need.

Create a function to represent the point [tex](x, y)[/tex] being reflected across the [tex]y[/tex]-axis.

[tex]F(x, y) = (-x, y)[/tex]

Sagot :

GinnyAnsweridn
Sure! Let's go through the process step by step to create a function that represents the point [tex]\((x, y)\)[/tex] being reflected across the [tex]\(y\)[/tex]-axis.

### Reflection Across the [tex]\(y\)[/tex]-Axis

When you reflect a point across the [tex]\(y\)[/tex]-axis, the [tex]\(x\)[/tex]-coordinate of the point changes sign, while the [tex]\(y\)[/tex]-coordinate remains the same.

For a point [tex]\((x, y)\)[/tex]:
- The reflected point will be [tex]\((-x, y)\)[/tex].

In mathematical terms, this transformation can be described by the function:

[tex]\[ F(x, y) = (-x, y) \][/tex]

### Step-by-Step Solution

1. Define the Input Coordinates:
- Let the original coordinates of the point be [tex]\((x, y)\)[/tex].

2. Reflect Across the [tex]\(y\)[/tex]-Axis:
- To find the reflected point, negate the [tex]\(x\)[/tex]-coordinate: [tex]\(-x\)[/tex].
- The [tex]\(y\)[/tex]-coordinate remains the same: [tex]\(y\)[/tex].

3. Formulate the Reflected Coordinates:
- The new coordinates after reflection will be [tex]\((-x, y)\)[/tex].

### Example

Let's work through an example to illustrate this:

Original Point:
- Suppose the original point is [tex]\((3, 4)\)[/tex].

Reflection Process:
- Negate the [tex]\(x\)[/tex]-coordinate: [tex]\(-3\)[/tex].
- Keep the [tex]\(y\)[/tex]-coordinate unchanged: [tex]\(4\)[/tex].

Reflected Point:
- The reflected point will be [tex]\((-3, 4)\)[/tex].

### General Function

To generalize this process for any point [tex]\((x, y)\)[/tex], we define a function [tex]\(F\)[/tex] as follows:

[tex]\[ F(x, y) = (-x, y) \][/tex]

So, if you are given any point [tex]\((x, y)\)[/tex] and you want to find the coordinates of the point after it has been reflected across the [tex]\(y\)[/tex]-axis, you simply apply the transformation provided by the function [tex]\(F\)[/tex].

### Conclusion
The function [tex]\(F(x, y) = (-x, y)\)[/tex] represents the point [tex]\((x, y)\)[/tex] being reflected across the [tex]\(y\)[/tex]-axis. This transformation changes the sign of the [tex]\(x\)[/tex]-coordinate and keeps the [tex]\(y\)[/tex]-coordinate unchanged.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.