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: Analyze horizontal translation

Observe the change in x - coordinates of corresponding points. For example, if we take a point in the pre - image and its corresponding point in the image, we see that the x - coordinate of each point in the image is 1 unit greater than the x - coordinate of the corresponding point in the pre - image. This means a right - hand shift of 1 unit, so the horizontal translation value is 1.

Step2: Analyze vertical translation

Observe the change in y - coordinates of corresponding points. The y - coordinate of each point in the image is 2 units greater than the y - coordinate of the corresponding point in the pre - image. This means an upward shift of 2 units, so the vertical translation value is 2.

Step3: Determine the translation rule

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

Answer:

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