Question

reasoning the translation (x,y) → (x + m,y + n) maps pq to pq.
write a rule for the translation of pq to pq.
(x,y) → (□,□)

Explanation:

Step1: Analyze the translation direction

Since \((x,y)\to(x + m,y + n)\) maps \(\overline{PQ}\) to \(\overline{P'Q'}\), to map \(\overline{P'Q'}\) back to \(\overline{PQ}\), we need to reverse the translation.

Step2: Reverse the translation

For the \(x\) - coordinate: if we had \(x\to x + m\) for the forward translation, for the reverse translation \(x\to x+(-m)\). For the \(y\) - coordinate: if we had \(y\to y + n\) for the forward translation, for the reverse translation \(y\to y+(-n)\)

Answer:

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