Question

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translation:(x,y)->(x-3,y-2) h(1,1) h(1,4) h(-2,-1) h(-2,3) h(-1,2)

Explanation:

Step1: Apply the translation rule to the x - coordinate

Given the translation rule \((x,y)\to(x - 3,y-2)\) and the point \(H(1,1)\). For the x - coordinate: \(x'=x - 3\). Substitute \(x = 1\) into the formula, we get \(x'=1-3=-2\).

Step2: Apply the translation rule to the y - coordinate

For the y - coordinate: \(y'=y - 2\). Substitute \(y = 1\) into the formula, we get \(y'=1 - 2=-1\).

Answer:

\(H'(-2,-1)\) (the blue - colored option)