Question

use the arrow notation to write a rule to describe the translation.

1. rule $(x,y)\to$ _ 2. rule $(x,y)\to$ _ 3. rule $(x,y)\to$ _

Explanation:

Step1: Find the translation for the first figure

Take a point, say \(A(-3,5)\) and \(A'(-3,-3)\). The \(x -\)coordinate remains the same (\(-3\)), and the \(y -\)coordinate changes from \(5\) to \(-3\). The change in \(y\) is \(y'=y - 8\). So the rule is \((x,y)\to(x,y - 8)\)

Step2: Find the translation for the second figure

Take a point \(B(6,1)\) and \(B'(-2,3)\). The change in \(x\) is \(x'=x-8\) (since \(6-8=-2\)) and the change in \(y\) is \(y'=y + 2\) (since \(1 + 2=3\)). So the rule is \((x,y)\to(x - 8,y+2)\)

Step3: Find the translation for the third figure

Take a point \(C(-6,1)\) and \(C'(2,1)\). The change in \(x\) is \(x'=x + 8\) (since \(-6+8 = 2\)) and the \(y -\)coordinate remains the same. So the rule is \((x,y)\to(x + 8,y)\)

Answer:

1. \((x,y)\to(x,y - 8)\)
2. \((x,y)\to(x - 8,y+2)\)
3. \((x,y)\to(x + 8,y)\)