Question

$\overline{fg}$ is reflected across the $y$-axis to produce $\overline{fg}$.

write the rule for the reflection.

$(x, y) \to \left(\square, \square\
ight)$

Explanation:

Step1: Recall reflection over y - axis rule

When a point \((x,y)\) is reflected across the \(y\) - axis, the \(y\) - coordinate remains the same, and the \(x\) - coordinate changes its sign.

Step2: Determine the transformation

For a reflection across the \(y\) - axis, if we have a point \((x,y)\), after reflection, the new \(x\) - coordinate is \(-x\) and the new \(y\) - coordinate is \(y\). So the rule is \((x,y)\to(-x,y)\).

Answer:

\((-x, y)\)