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To find the perimeter of the triangle formed by points A(-4, 3), B(3, 3), and C(-2, -3), we will first calculate the lengths of the three sides of the triangle using the distance formula:

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

### Step 1: Find the distance between A and B
\[
A(-4, 3), B(3, 3)
\]
\[
AB = \sqrt{(3 - (-4))^2 + (3 - 3)^2} = \sqrt{(3 + 4)^2 + 0^2} = \sqrt{7^2} = 7
\]

### Step 2: Find the distance between B and C
\[
B(3, 3), C(-2, -3)
\]
\[
BC = \sqrt{(-2 - 3)^2 + (-3 - 3)^2} = \sqrt{(-5)^2 + (-6)^2} = \sqrt{25 + 36} = \sqrt{61} \approx 7.81
\]

### Step 3: Find the distance between A and C
\[
A(-4, 3), C(-2, -3)
\]
\[
AC = \sqrt{(-2 - (-4))^2 + (-3 - 3)^2} = \sqrt{(2)^2 + (-6)^2} = \sqrt{4 + 36} = \sqrt{40} \approx 6.32
\]

### Step 4: Find the perimeter
Now, sum the lengths of the sides:
\[
\text{Perimeter} = AB + BC + AC = 7 + 7.81 + 6.32 = 21.13
\]

Thus, the perimeter is approximately **21.1**.

### The correct answer is **21.1**.

Let me know if you'd like further details or have any questions! 

Here are some related questions you might find interesting:
1. How does the distance formula apply to 3-dimensional coordinates?
2. What would be the perimeter of a quadrilateral if given its vertices?
3. How can you determine if a triangle is right-angled using distance formulas?
4. How do you calculate the area of a triangle given its vertices?
5. What is the significance of the Pythagorean theorem in triangle perimeter calculations?

**Tip**: When calculating the perimeter of a polygon, always ensure you apply the distance formula between each consecutive pair of points and then sum the lengths!

Find the perimeter of the triangle with vertices A(-4,3), B(3,3), and C(-2,-3) to one decimal point.

Learn how to calculate the perimeter of a triangle with vertices A(-4,3), B(3,3), and C(-2,-3) using the distance formula. This step-by-step guide is suitable for students in Grades 8-10 and covers key concepts in coordinate geometry.

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