Answered

Given the nature of the text, it appears to be a collection of sets of ordered pairs. To improve readability and maintain the structure, I will format it in a clearer way:

[tex]\[
\begin{array}{l}
\{(2, -2), (1, 5), (-2, 2), (1, -3), (8, -1)\} \\
\{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)\} \\
\{(6, 8), (5, 2), (-2, -5), (1, -3), (-2, 9)\} \\
\{(-3, 1), (6, 3), (-3, 2), (-3, -3), (1, -1)\}
\end{array}
\][/tex]

This format retains all the necessary information while making it easier to read.



Answer :

GinnyAnswer
To solve this task, we need to find the average of the x-coordinates and y-coordinates for each set of given points. Here's a step-by-step breakdown of how you can find these averages for each set:

### Set 1: [tex]\(\{(2,-2),(1,5),(-2,2),(1,-3),(8,-1)\}\)[/tex]

1. Identify the x-coordinates: 2, 1, -2, 1, 8
2. Identify the y-coordinates: -2, 5, 2, -3, -1

Calculate the average x-coordinate:

[tex]\[ \text{Average } x = \frac{2 + 1 - 2 + 1 + 8}{5} = \frac{10}{5} = 2.0 \][/tex]

Calculate the average y-coordinate:

[tex]\[ \text{Average } y = \frac{-2 + 5 + 2 - 3 - 1}{5} = \frac{1}{5} = 0.2 \][/tex]

So, the average for Set 1 is [tex]\((2.0, 0.2)\)[/tex].

---

### Set 2: [tex]\(\{(3,-1),(7,1),(-6,-1),(9,1),(2,-1)\}\)[/tex]

1. Identify the x-coordinates: 3, 7, -6, 9, 2
2. Identify the y-coordinates: -1, 1, -1, 1, -1

Calculate the average x-coordinate:

[tex]\[ \text{Average } x = \frac{3 + 7 - 6 + 9 + 2}{5} = \frac{15}{5} = 3.0 \][/tex]

Calculate the average y-coordinate:

[tex]\[ \text{Average } y = \frac{-1 + 1 - 1 + 1 - 1}{5} = \frac{-1}{5} = -0.2 \][/tex]

So, the average for Set 2 is [tex]\((3.0, -0.2)\)[/tex].

---

### Set 3: [tex]\(\{(6,8),(5,2),(-2,-5),(1,-3),(-2,9)\}\)[/tex]

1. Identify the x-coordinates: 6, 5, -2, 1, -2
2. Identify the y-coordinates: 8, 2, -5, -3, 9

Calculate the average x-coordinate:

[tex]\[ \text{Average } x = \frac{6 + 5 - 2 + 1 - 2}{5} = \frac{8}{5} = 1.6 \][/tex]

Calculate the average y-coordinate:

[tex]\[ \text{Average } y = \frac{8 + 2 - 5 - 3 + 9}{5} = \frac{11}{5} = 2.2 \][/tex]

So, the average for Set 3 is [tex]\((1.6, 2.2)\)[/tex].

---

### Set 4: [tex]\(\{(-3,1),(6,3),(-3,2),(-3,-3),(1,-1)\}\)[/tex]

1. Identify the x-coordinates: -3, 6, -3, -3, 1
2. Identify the y-coordinates: 1, 3, 2, -3, -1

Calculate the average x-coordinate:

[tex]\[ \text{Average } x = \frac{-3 + 6 - 3 - 3 + 1}{5} = \frac{-2}{5} = -0.4 \][/tex]

Calculate the average y-coordinate:

[tex]\[ \text{Average } y = \frac{1 + 3 + 2 - 3 - 1}{5} = \frac{2}{5} = 0.4 \][/tex]

So, the average for Set 4 is [tex]\((-0.4, 0.4)\)[/tex].

Hence, the averages for the four sets of points are:

[tex]\[ ((2.0, 0.2), (3.0, -0.2), (1.6, 2.2), (-0.4, 0.4)) \][/tex]

These are the average coordinates for each set of points provided.

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