What’s the perimeter of the quadrilateral if one point is (-2,1) one is (3,1) one is (3,-7) and one is (-2,-7)

To find the perimeter of the quadrilateral with the given vertices, we'll calculate the distance between each pair of adjacent points, then sum these distances.

The vertices are:
- \( A(-2, 1) \)
- \( B(3, 1) \)
- \( C(3, -7) \)
- \( D(-2, -7) \)

### Step 1: Calculate the distances between adjacent points.
1. **Distance \( AB \)**:
   \[
   AB = \sqrt{(3 - (-2))^2 + (1 - 1)^2} = \sqrt{(3 + 2)^2 + 0^2} = \sqrt{5^2} = 5
   \]

2. **Distance \( BC \)**:
   \[
   BC = \sqrt{(3 - 3)^2 + (-7 - 1)^2} = \sqrt{0^2 + (-8)^2} = \sqrt{64} = 8
   \]

3. **Distance \( CD \)**:
   \[
   CD = \sqrt{(-2 - 3)^2 + (-7 - (-7))^2} = \sqrt{(-5)^2 + 0^2} = \sqrt{25} = 5
   \]

4. **Distance \( DA \)**:
   \[
   DA = \sqrt{(-2 - (-2))^2 + (1 - (-7))^2} = \sqrt{0^2 + 8^2} = \sqrt{64} = 8
   \]

### Step 2: Calculate the perimeter.
The perimeter \( P \) is the sum of the distances:
\[
P = AB + BC + CD + DA = 5 + 8 + 5 + 8 = 26
\]

### Final Answer:
The perimeter of the quadrilateral is \( \boxed{26} \).

Would you like more details on any part of the solution? Here are five related questions to deepen your understanding:

1. How do you calculate the distance between any two points in a coordinate plane?
2. What is the difference between the perimeter and the area of a shape?
3. How would the perimeter change if the coordinates of one point were different?
4. Can the perimeter formula be generalized for any quadrilateral in a coordinate plane?
5. How would you find the perimeter if the quadrilateral were not axis-aligned?

**Tip:** Always ensure you have the correct order of vertices when calculating the perimeter of a polygon to avoid missing sides or duplicating them.

Learn how to calculate the perimeter of a quadrilateral with given vertices (-2, 1), (3, 1), (3, -7), and (-2, -7). This problem covers coordinate geometry, including the distance formula and perimeter calculation for polygons. Suitable for Grades 7-9 students.

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