The problem describes geometric transformations in animations. It asks to find the translations that map one shape to another based on their coordinates on a graph. Specifically, we need to: 1. Find the translation that maps shape 1 to shape 5.

1. Problem Description

The problem describes geometric transformations in animations. It asks to find the translations that map one shape to another based on their coordinates on a graph. Specifically, we need to:

1. Find the translation that maps shape 1 to shape

5.

2. Find the translation that maps shape 1 to shape

4.

3. Find the translation that maps shape 2 to shape

3.

2. Solution Steps

First, let's identify the coordinates of each shape:

Shape 1: (-2, -2)

Shape 2: (1, 0)

Shape 3: (4, -2)

Shape 4: (4, 2)

Shape 5: (4, 3)

1. Finding the translation from Shape 1 to Shape 5:

To find the translation, we need to determine the changes in the x and y coordinates. Let the translation be $(x, y) \rightarrow (x + a, y + b)$.

Shape 1: (-2, -2)

Shape 5: (4, 3)

So, we have:

$-2 + a = 4$, which gives $a = 6$

$-2 + b = 3$, which gives $b = 5$

The translation is $(x, y) \rightarrow (x + 6, y + 5)$.

2. Finding the translation from Shape 1 to Shape 4:

Shape 1: (-2, -2)

Shape 4: (4, 2)

So, we have:

$-2 + a = 4$, which gives $a = 6$

$-2 + b = 2$, which gives $b = 4$

The translation is $(x, y) \rightarrow (x + 6, y + 4)$.

3. Finding the translation from Shape 2 to Shape 3:

Shape 2: (1, 0)

Shape 3: (4, -2)

So, we have:

$1 + a = 4$, which gives $a = 3$

$0 + b = -2$, which gives $b = -2$

The translation is $(x, y) \rightarrow (x + 3, y - 2)$.

3. Final Answer

1. The translation that makes shape 5 the image of shape 1 is $(x, y) \rightarrow (x + 6, y + 5)$.

2. The translation that makes shape 4 the image of shape 1 is $(x, y) \rightarrow (x + 6, y + 4)$.

3. The translation that makes shape 3 the image of shape 2 is $(x, y) \rightarrow (x + 3, y - 2)$.