Question

which translation rule describes the translation from efgh → efgh? (x - 2,y + 1) (x + 3,y - 1) (x + 1,y - 2) (x - 1,y + 2)

Explanation:

Step1: Observe x - coordinate change

Take a point, say E. Let the coordinates of E be \((x_1,y_1)\) and of \(E'\) be \((x_2,y_2)\). By looking at the graph, if we assume E is at \((1,2)\) and \(E'\) is at \((- 1,3)\). The change in the x - coordinate is \(x_2-x_1=-1 - 1=-2\).

Step2: Observe y - coordinate change

The change in the y - coordinate is \(y_2 - y_1=3 - 2 = 1\).

Step3: Determine the translation rule

The general translation rule is \((x,y)\to(x + a,y + b)\), where \(a\) is the change in the x - coordinate and \(b\) is the change in the y - coordinate. Here \(a=-2\) and \(b = 1\), so the rule is \((x-2,y + 1)\).

Answer:

\((x - 2,y + 1)\)