Question

write a rule to describe each transformation.

Explanation:

Step1: Analyze the first transformation

For the first figure, observe the change in coordinates of corresponding points. Let's assume a general point $(x,y)$ on the original figure. If we look at the vertical movement of points, we can see that the $y -$coordinate of each point on the new figure is obtained by subtracting a certain value from the $y -$coordinate of the corresponding point on the original figure. Counting the grid - squares, we find that each point is moved 4 units down. So the transformation rule is $(x,y)\to(x,y - 4)$.

Step2: Analyze the second transformation

For the second figure, consider a general point $(x,y)$ on the original figure. Notice that the new figure is a reflection of the original figure across the $y -$axis. When a point $(x,y)$ is reflected across the $y -$axis, the $x -$coordinate changes its sign while the $y -$coordinate remains the same. So the transformation rule is $(x,y)\to(-x,y)$.

Answer:

1. $(x,y)\to(x,y - 4)$
2. $(x,y)\to(-x,y)$