Question

2 choos the rule that represents a reflection across the y-axis.
$(x, y) \to \boxed{\quad}$
a $(-x, -y)$
b $(y, -x)$
c $(-x, y)$
d $(x, -y)$

Explanation:

To determine the rule for reflection across the \( y \)-axis, we recall the transformation rule: when a point \((x, y)\) is reflected across the \( y \)-axis, the \( x \)-coordinate changes its sign (becomes \(-x\)) while the \( y \)-coordinate remains the same (\( y \)).

• Option A: \((-x, -y)\) is a reflection across the origin (both \( x \) and \( y \) change sign), not the \( y \)-axis.
• Option B: \((y, -x)\) is a rotation or a different transformation, not a reflection across the \( y \)-axis.
• Option C: \((-x, y)\) matches the rule for reflection across the \( y \)-axis ( \( x \)-coordinate is negated, \( y \)-coordinate stays the same).
• Option D: \((x, -y)\) is a reflection across the \( x \)-axis ( \( y \)-coordinate changes sign), not the \( y \)-axis.

Answer:

C. \((-x, y)\)