To determine the rule of the transformation from figure 1 to figure 2, we can follow these steps:

1. Analyze the translation

A translation moves a figure horizontally and/or vertically without changing its shape or orientation.

• From the graph:
  • Figure 1 (on the left) is moved to Figure 2 (on the right).
  • To determine the translation rule, pick a vertex (corner) from figure 1 and identify where it moves in figure 2.

2. Track the movement of a point

Let’s choose a specific vertex of the triangle in figure 1:

• Pick the point at (-5, 1) in figure 1.
• This vertex has been translated to the point (3, -3) in figure 2.

3. Find the horizontal and vertical shifts

To determine the translation rule:

1. Horizontal movement (x-direction):
   From $x = -5$ to $x = 3$:
   $3 - (-5) = 8 \quad \text{(move right by 8 units)}.$

2. Vertical movement (y-direction):
   From $y = 1$ to $y = -3$:
   $-3 - 1 = -4 \quad \text{(move down by 4 units)}.$

4. Write the transformation rule

The transformation can be described as:
$(x, y) \to (x + 8, y - 4).$

Thus, the boxes to fill in are:
(x + 8, y - 4).

Final Answer:

$(x, y) \to (x + 8, y - 4)$

Let me know if you want me to explain further! Here are some related questions:

1. What is the definition of a translation in geometry?
2. How do you determine the horizontal and vertical shifts in a transformation?
3. Can this transformation be represented in vector form?
4. How would the rule change if the translation were in the opposite direction?
5. How can translations be used to solve real-world geometry problems?

Tip: Always track a specific vertex or point in translations to easily find the movement!