Question

determine the rule for each translation. * (x + 1, y - 3) (x + 4, y) (x - 1, y + 1) (x, y + 4) (x - 1, y - 1) (x, y - 4) (x + 2, y + 1) (x + 1, y + 3) (x + 1, y + 1) (x - 2, y - 1) (x + 4, y + 4) (x + 2, y - 1) (x - 4, y) (x - 1, y - 3)

Explanation:

Step1: Find coordinates of a point

Let's take point \( L\). Assume \( L\) has coordinates \((x_1,y_1)\). From the graph, if we assume \( L=( - 1,3)\) (by counting grid - squares from the origin). And its image \( L'\) has coordinates \((x_2,y_2)\). If \( L'=(3, - 1)\) (by counting grid - squares from the origin).

Step2: Calculate the change in \(x\) and \(y\)

The change in \(x\) is \(\Delta x=x_2 - x_1=3-( - 1)=4\). The change in \(y\) is \(\Delta y=y_2 - y_1=-1 - 3=-4\).

Answer:

\((x + 4,y-4)\) is not in the given options. Let's check another way.
Take point \(A\). Assume \(A=(4,5)\) (by counting grid - squares from the origin). And its image \(A'=(5,2)\) (by counting grid - squares from the origin).
The change in \(x\) is \(\Delta x = 5-4=1\). The change in \(y\) is \(\Delta y=2 - 5=-3\).
The translation rule is \((x + 1,y-3)\)