Question

write a rule for the translation that maps each figure to its image.
2.
3.

Explanation:

Step1: Find the translation of a point in problem 2

Take point \(A(1,0)\) and its image \(A'(1,4)\). The \(x -\)coordinate remains the same (\(1 - 1=0\)), and the \(y -\)coordinate changes from \(0\) to \(4\) (\(4 - 0 = 4\)).

Step2: Write the translation rule for problem 2

The rule for a translation is \((x,y)\to(x,y + k)\). Here \(k = 4\), so the rule is \((x,y)\to(x,y+4)\)

Step3: Find the translation of a point in problem 3

Take point \(B(-1,3)\) and its image \(B'(1,-2)\). The change in \(x\) is \(1-(-1)=2\), and the change in \(y\) is \(-2 - 3=-5\)

Step4: Write the translation rule for problem 3

The rule for a translation is \((x,y)\to(x + h,y + k)\). Here \(h = 2\) and \(k=-5\), so the rule is \((x,y)\to(x + 2,y-5)\)

Answer:

1. \((x,y)\to(x,y + 4)\)
2. \((x,y)\to(x + 2,y-5)\)