Question

hexagon cdefgh is reflected across the x-axis to produce hexagon cdefgh. write the rule for the reflection. (x, y) → (\square, \square)

Explanation:

Step1: Recall reflection over x - axis rule

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

Step2: Apply the rule to the general point \((x,y)\)

For a point \((x,y)\) in the coordinate plane, after reflection across the \(x\) - axis, the new coordinates \((x',y')\) are given by \(x'=x\) and \(y'=-y\). So the rule for reflection across the \(x\) - axis is \((x,y)\to(x, - y)\).

Answer:

\((x, - y)\)