Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Which point would map onto itself after a reflection across the line [tex]y = -x[/tex]?

A. [tex](-4, -4)[/tex]
B. [tex](-4, 0)[/tex]
C. [tex](0, -4)[/tex]
D. [tex](4, -4)[/tex]

Sagot :

GinnyAnswer
To determine which point maps onto itself after a reflection across the line \( y = -x \), we need to understand the reflection process. For a point \((x, y)\), the reflection across the line \( y = -x \) is \((-y, -x)\).

Let's check each given point:

1. \((-4, -4)\)
- Reflect \((-4, -4)\) across \( y = -x \).
- The reflection is \((-(-4), -(-4)) = (4, 4)\).
- Thus, \((-4, -4)\) does not map onto itself.

2. \((-4, 0)\)
- Reflect \((-4, 0)\) across \( y = -x \).
- The reflection is \((0, -(-4)) = (0, 4)\).
- Thus, \((-4, 0)\) does not map onto itself.

3. \((0, -4)\)
- Reflect \((0, -4)\) across \( y = -x \).
- The reflection is \((-(-4), -(0)) = (4, 0)\).
- Thus, \((0, -4)\) does not map onto itself.

4. \((4, -4)\)
- Reflect \((4, -4)\) across \( y = -x \).
- The reflection is \((-(-4), -4) = (4, -4)\).
- Thus, \((4, -4)\) does map onto itself.

Therefore, the point that maps onto itself after a reflection across the line [tex]\( y = -x \)[/tex] is [tex]\( (4, -4) \)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.