https://file.aiquickdraw.com/mathbot/file/17262518193972lloa93d.jpg

The problem asks for the perimeter of quadrilateral **JKLM** with vertices at the points:

- \( J(-3, -2) \)
- \( K(-5, -5) \)
- \( L(1, -5) \)
- \( M(3, -2) \)

### Steps to find the perimeter:

1. **Find the lengths of the sides** using the distance formula for each pair of vertices. The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

2. **Apply the distance formula** for the following pairs of vertices (the sides of the quadrilateral):
   - **JK** (between \( J(-3, -2) \) and \( K(-5, -5) \))
   - **KL** (between \( K(-5, -5) \) and \( L(1, -5) \))
   - **LM** (between \( L(1, -5) \) and \( M(3, -2) \))
   - **MJ** (between \( M(3, -2) \) and \( J(-3, -2) \))

3. **Sum the lengths** of the sides to get the perimeter.

Let me calculate that for you.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can guide you step-by-step on how to calculate the perimeter manually.

Do you want to proceed with manual steps, or have other questions?

Here are 5 related questions:
1. How is the distance formula derived from the Pythagorean theorem?
2. What other geometric shapes can you calculate perimeter for using the distance formula?
3. Can you apply the midpoint formula in this problem? How would you use it?
4. What is the difference between finding the perimeter and the area of a quadrilateral?
5. How can you verify your calculations when solving for distance?

**Tip:** Always write down each calculation clearly when working through complex multi-step problems, so you can spot any errors easily!

Find the perimeter of quadrilateral JKLM with vertices J(-3, -2), K(-5, -5), L(1, -5), and M(3, -2).

Learn how to calculate the perimeter of quadrilateral JKLM with vertices at J(-3, -2), K(-5, -5), L(1, -5), and M(3, -2) using the distance formula. This problem involves key geometric concepts like the distance formula and the perimeter of quadrilaterals. Ideal for students in Grades 9-10.

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