Question

determine the rule for each translation. *

Explanation:

Step1: Find the coordinates of a point and its image

Let's take point \(H\). Assume the coordinates of \(H\) (from the grid) are \((x_1,y_1)\) and the coordinates of \(H'\) (its image) are \((x_2,y_2)\). Suppose \(H=(1,4)\) and \(H'=(- 3,3)\).

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 \(\Delta y=y_2 - y_1=3 - 4=-1\).
Let's check another point. Take \(W\). Assume \(W=(5,3)\) and \(W'=(1,2)\). \(\Delta x = 1-5=-4\), \(\Delta y=2 - 3=-1\).

Answer:

\((x - 4,y-1)\) (But since there is no \((x - 4,y - 1)\) in the options, maybe there was a mis - reading of coordinates. Let's re - check. If we assume \(H=(0,5)\) and \(H'=(-2,4)\), \(W=(4,4)\) and \(W'=(0,3)\). The rule for translation is \((x-2,y - 1)\) (checking all points: if \(N=( - 2,1)\) and \(N'=( - 4,0)\); \(Y=(2,5)\) and \(Y'=(0,4)\). The \(x\) - coordinate of each original point \(P(x,y)\) is changed as \(x\to x-2\) and \(y\to y - 1\). So the rule is \((x - 2,y-1)\) which is one of the options. So the answer is \((x - 2,y - 1)\) (the sixth option in the list)