Question

q. which rule correctly describes this translation?

Explanation:

Step1: Observe the change in x - coordinates

Count the horizontal shift of a point on the pre - image to its corresponding point on the image. For example, if we take a vertex of the pre - image polygon and its corresponding vertex on the image polygon, we see that the x - coordinate of each point in the pre - image decreases by a certain value.

Step2: Observe the change in y - coordinates

Count the vertical shift of a point on the pre - image to its corresponding point on the image. We find that the y - coordinate of each point in the pre - image decreases by a certain value.
Let's assume a general point \((x,y)\) in the pre - image. If the figure is shifted \(a\) units to the left (negative x - direction) and \(b\) units down (negative y - direction), the translation rule is \((x,y)\to(x - a,y - b)\).
By observing the grid, if we take a vertex of the upper - left figure (pre - image) and its corresponding vertex on the lower - right figure (image), we can see that the figure is shifted 4 units to the left and 5 units down. So the rule is \((x,y)\to(x - 4,y - 5)\)

Answer:

\((x,y)\to(x - 4,y - 5)\)