Question

(x, y) → ( , )
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Explanation:

Step1: Identify coordinates of corresponding points

Let's assume \(E(- 4, - 2)\) and \(E'(5,10)\), \(F(-2,-7)\) and \(F'(6,4)\), \(G(-8,-9)\) and \(G'(1,2)\).

Step2: Find the change in \(x\) - coordinate

For point \(E\) to \(E'\), \(\Delta x=5 - (-4)=9\). For point \(F\) to \(F'\), \(\Delta x = 6-(-2)=8\). For point \(G\) to \(G'\), \(\Delta x=1 - (-8)=9\).

Step3: Find the change in \(y\) - coordinate

For point \(E\) to \(E'\), \(\Delta y=10-(-2)=12\). For point \(F\) to \(F'\), \(\Delta y = 4-(-7)=11\). For point \(G\) to \(G'\), \(\Delta y=2-(-9)=11\).

Step4: Determine the transformation rule

The transformation rule from \((x,y)\) to \((x + 9,y + 11)\)

Answer:

\((x + 9,y + 11)\)