Question

1. rule $(x,y)\to$ ________

1. rule $(x,y)\to$ ________

1. rule $(x,y)\to$ ________

Explanation:

Step1: Analyze the \(x\) - coordinate change for problem 4

For point \(A(-3,4)\) and \(A'(0,2)\), \(x\) - coordinate: \(0-(-3)=3\). For point \(B(-5,4)\) and \(B'(-2,2)\), \(x\) - coordinate: \(-2 - (-5)=3\). For point \(C(-5,1)\) and \(C'(-2,-1)\), \(x\) - coordinate: \(-2-(-5) = 3\).
For \(y\) - coordinate: \(2 - 4=-2\), \(2 - 4=-2\), \(-1 - 1=-2\).
The rule is \((x,y)\to(x + 3,y-2)\)

Step2: Analyze the \(x\) - coordinate change for problem 5

For point \(A(4,3)\) and \(A'(6,4)\), \(x\) - coordinate: \(6 - 4=2\). For point \(B(2,3)\) and \(B'(4,4)\), \(x\) - coordinate: \(4 - 2=2\). For point \(C(3,0)\) and \(C'(5,1)\), \(x\) - coordinate: \(5 - 3=2\).
For \(y\) - coordinate: \(4 - 3=1\), \(4 - 3=1\), \(1-0 = 1\).
The rule is \((x,y)\to(x + 2,y + 1)\)

Step3: Analyze the \(x\) - coordinate change for problem 6

For point \(A(5,5)\) and \(A'(1,9)\), \(x\) - coordinate: \(1-5=-4\). For point \(B(3,4)\) and \(B'(-1,8)\), \(x\) - coordinate: \(-1 - 3=-4\). For point \(C(4,2)\) and \(C'(0,6)\), \(x\) - coordinate: \(0 - 4=-4\).
For \(y\) - coordinate: \(9 - 5=4\), \(8 - 4=4\), \(6 - 2=4\).
The rule is \((x,y)\to(x-4,y + 4)\)

Answer:

1. \((x,y)\to(x + 3,y-2)\)
2. \((x,y)\to(x + 2,y + 1)\)
3. \((x,y)\to(x-4,y + 4)\)