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(x, y) → ( , )

Explanation:

1. First, identify the coordinates of the pre - image and image points:

• Let's assume a point \(W(x_1,y_1)\) and its image \(W'(x_2,y_2)\). From the graph, if we assume \(W(- 4,-9)\) and \(W'(0,-1)\), and another point \(X(-4,-4)\) and its image \(X'(0,4)\).
• For the \(x\) - coordinates:
• The change in the \(x\) - coordinate from \(W\) to \(W'\) is \(\Delta x=x_2 - x_1=0-(-4)=4\).
• The change in the \(x\) - coordinate from \(X\) to \(X'\) is also \(0 - (-4)=4\).
• For the \(y\) - coordinates:
• The change in the \(y\) - coordinate from \(W\) to \(W'\) is \(\Delta y=y_2 - y_1=-1-(-9)=8\).
• The change in the \(y\) - coordinate from \(X\) to \(X'\) is \(4-(-4)=8\).

1. Determine the transformation rule \((x,y)\to(x + a,y + b)\):

• Since the change in the \(x\) - coordinate (\(a\)) is \(4\) and the change in the \(y\) - coordinate (\(b\)) is \(8\), the transformation rule is \((x,y)\to(x + 4,y + 8)\).

Step1: Find change in x - coordinates

For points \(W\) and \(W'\) (or \(X\) and \(X'\)), calculate \(x_{image}-x_{pre - image}\). For \(W(-4,-9)\) and \(W'(0,-1)\), \(0-(-4)=4\).

Step2: Find change in y - coordinates

For points \(W\) and \(W'\) (or \(X\) and \(X'\)), calculate \(y_{image}-y_{pre - image}\). For \(W(-4,-9)\) and \(W'(0,-1)\), \(-1-(-9)=8\).

Step3: Write transformation rule

The rule \((x,y)\to(x + 4,y + 8)\) is based on the changes found in \(x\) and \(y\) coordinates.

Answer:

\((x,y)\to(x + 4,y + 8)\)