Question

which rule represents the translation from the pre - image, ▱abcd, to the image, ▱abcd?
t_{1,-2}(x,y)
t_{1,2}(x,y)
t_{-2,1}(x,y)
t_{2,1}(x,y)

Explanation:

Step1: Observe x - coordinate change

Pick a vertex, say A. Its x - coordinate in pre - image is about - 3 and in image is about - 2. The change in x - coordinate $\Delta x=-2-(-3) = 1$.

Step2: Observe y - coordinate change

The y - coordinate of A in pre - image is about 5 and in image is about 7. The change in y - coordinate $\Delta y=7 - 5=2$.

Step3: Determine translation rule

The translation rule $T_{a,b}(x,y)=(x + a,y + b)$ where $a = 1$ and $b = 2$, so the rule is $T_{1,2}(x,y)$.

Answer:

$T_{1,2}(x,y)$