Question

write a rule to describe each transformation.
5)
6)

Explanation:

Step1: Analyze the horizontal and vertical changes for problem 5

Let's assume a general point \((x,y)\) in the original figure. For example, if we look at the movement of point \(B\) to \(B'\). Count the units moved horizontally and vertically.
If we consider the translation rule \((x,y)\to(x + a,y + b)\). By observing the grid, we can see that for each point, the \(x\)-coordinate increases by \(2\) (right - ward movement) and the \(y\)-coordinate remains the same. So the rule is \((x,y)\to(x + 2,y)\)

Step2: Analyze the horizontal and vertical changes for problem 6

Let's assume a general point \((x,y)\) in the original figure. For example, if we look at the movement of point \(D\) to \(D'\). Count the units moved horizontally and vertically.
If we consider the translation rule \((x,y)\to(x + a,y + b)\). By observing the grid, we can see that for each point, the \(x\)-coordinate increases by \(6\) (right - ward movement) and the \(y\)-coordinate remains the same. So the rule is \((x,y)\to(x + 6,y)\)

Answer:

1. \((x,y)\to(x + 2,y)\)
2. \((x,y)\to(x + 6,y)\)