Question

irina wants to tile her floor using the translation shown below. which is the rule for this translation? o $t_{-3,2}(x,y)$ o $t_{2,-3}(x,y)$ o $t_{3,2}(x,y)$ o $t_{-2,3}(x,y)$

Explanation:

Step1: Observe x - coordinate change

To find the translation rule, we look at how the x - coordinate of a point changes. Let's take a point on the original shape (e.g., point A). If we assume the original point A has coordinates \((x,y)\) and its new - position \(A'\) has coordinates \((x + a,y + b)\). By observing the graph, for a point on the original shape, the x - coordinate of the corresponding point on the translated shape decreases by 3. So \(a=-3\).

Step2: Observe y - coordinate change

Now, look at the y - coordinate change. The y - coordinate of the corresponding point on the translated shape increases by 2. So \(b = 2\).

Step3: Determine the translation rule

The general form of a translation is \(T_{a,b}(x,y)=(x + a,y + b)\). Substituting \(a=-3\) and \(b = 2\), we get \(T_{-3,2}(x,y)\).

Answer:

\(T_{-3,2}(x,y)\)