Question

Which algebraic rule describes the reflection of The text that reads: The line FG. ?
An image displaying a line FG intersecting with line F'G'. The vertices of FG is F of -6 comma -3 and G of 3 comma 6. the vertice s of F'G' is F' of 6 comma -3 and G' of -3 comma 6. They intersect at 0 comma 3.
A.
(x, y) → (x, −y)
B.
(x, y) → (−x, y)
C.
(x, y) → (x − 1, y − 1)
D.
(x, y) → (1 − x, 1 − y)

Answer 1

To determine which algebraic rule describes the reflection of the text "The line FG", we can analyze the points given:

- Original points:
- \( F(-6, -3) \)
- \( G(3, 6) \)

- Reflected points:
- \( F'(6, -3) \)
- \( G'(-3, 6) \)

The intersection point \( (0, 3) \) suggests that this transformation involves reflection across a specific line.

If we look at the points:
- For point \( F \) which is \( (-6, -3) \) to become \( F'(6, -3) \), the x-coordinate changes from -6 to 6, which is a reflection across the y-axis.
- For point \( G \) which is \( (3, 6) \) to become \( G'(-3, 6) \), the x-coordinate also changes from 3 to -3, again indicating it reflects across the y-axis.

Thus, the reflection can be described using the rule:
\[
(x, y) \rightarrow (-x, y)
\]
This corresponds to option B:
\[
B. (x, y) → (−x, y)
\]

This transformation reflects the points across the y-axis. Therefore, the correct answer is **B. (x, y) → (−x, y)**.