Question

What is the rule for the reflection? A) ry=x(x, y) → (–y, –x) B) ry=–x(x, y) → (–y, –x) C) ry=x(x, y) → (y, x) D) ry=–x(x, y) → (y, x) If you can help, it'd be greatly appreciated.What is the rule for the reflection?

- A) \( r_y = x \) (\( x, y \) → \( -y, -x \))
- B) \( r_y = -x \) (\( x, y \) → \( -y, -x \))
- C) \( r_y = x \) (\( x, y \) → \( y, x \))
- D) \( r_y = -x \) (\( x, y \) → \( y, x \))

Answer 1

The given options are incorrect, but the rule for reflection across the y-axis should map a point (x, y) to (-x, y), which is not represented in any of the provided answers.

Step-by-step explanation:

The rule for reflection across the y-axis is most accurately represented in option B, which states ry = -x(x, y) → (-y, -x). When we reflect a point across the y-axis, the x-coordinate changes sign, but the y-coordinate remains the same. However, option B includes an error because the reflection across the y-axis should actually map point (x, y) to point (-x, y), not (-y, -x) as stated. Therefore, none of the given options are completely accurate. The correct reflection rule when reflecting a point across the y-axis should be (x, y) → (-x, y), which is not listed among the options provided.

Reflection across other axes will have different rules. For example, reflecting across the x-axis maps point (x, y) to point (x, -y). It is important to take note of which axis the reflection is occurring over to apply the correct transformation.