Question

find a translation that has the same effect as the composition of translations (x,y) → (x + 5,y + 3) followed by (x,y) → (x - 6,y + 8).
complete the translation rule.
(x,y) →

Explanation:

Step1: First translation result

Let the point \((x,y)\) be translated by \((x,y)\to(x + 5,y+3)\). The new - point is \((x_1,y_1)=(x + 5,y + 3)\).

Step2: Apply second translation

Now, apply the second translation \((x,y)\to(x - 6,y + 8)\) to the point \((x_1,y_1)\). Replace \(x\) with \(x_1=x + 5\) and \(y\) with \(y_1=y + 3\) in the second - translation rule.
We get \(x_2=(x + 5)-6=x+5 - 6=x - 1\) and \(y_2=(y + 3)+8=y+3 + 8=y + 11\).

Answer:

\((x,y)\to(x - 1,y + 11)\)