Question

pq is reflected across the y - axis to produce pq. write the rule for the reflection. (x, y) → ( , )

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is that the \(y\) - coordinate remains the same, and the \(x\) - coordinate changes its sign. Mathematically, if a point \((x,y)\) is reflected over the \(y\) - axis, the image of the point is \((-x,y)\).

Step2: Verify with the graph

Looking at the graph, when we reflect a point from the right side of the \(y\) - axis (positive \(x\) - values) to the left side (negative \(x\) - values), the \(y\) - coordinate of the points on the line segment \(PQ\) and its image \(P'Q'\) remains unchanged, while the \(x\) - coordinate is negated. For example, if we take a point on \(PQ\) with coordinates \((x,y)\), after reflection over the \(y\) - axis, it moves to \((-x,y)\) on \(P'Q'\).

Answer:

\((x,y)\to(-x,y)\)