Question

Use the image to answer the question.

A coordinate plane shows the x-axis ranging from negative 9 to 9 in unit increments and the y-axis ranging from negative 11 to 11 in unit increments. Six plotted points are joined to form a composite figure. The six plotted points are upper A, upper B, upper C, upper D, upper E, and upper F. The coordinates of the plotted points are as follows: point upper A is left parenthesis 2 comma negative 6 right parenthesis, point upper B is left parenthesis negative 5 comma negative 6 right parenthesis, point upper C is left parenthesis negative 5 comma 6 right parenthesis, point upper D is left parenthesis 6 comma 6 right parenthesis, point upper E is left parenthesis 6 comma 1 right parenthesis, and point upper F is left parenthesis 2 comma 1 right parenthesis.

Find the perimeter of the polygon in kilometers.

(1 point)
Responses

104 square kilometers
104 square kilometers

34 square kilometers
34 square kilometers

46 square kilometers
46 square kilometers

46 kilometers

Answer 1

To find the perimeter of the polygon formed by the points A, B, C, D, E, and F on the coordinate plane, we first need to determine the distances between each pair of consecutive points. We will then add these distances to get the total perimeter.

The coordinates of the points are:
- A (2, -6)
- B (-5, -6)
- C (-5, 6)
- D (6, 6)
- E (6, 1)
- F (2, 1)

Now let's calculate the distances between consecutive points.

1. **Distance AB**:
\[
\sqrt{((-5 - 2)^2 + (-6 - (-6))^2)} = \sqrt{(-7)^2 + 0^2} = \sqrt{49} = 7
\]

2. **Distance BC**:
\[
\sqrt{((-5 - (-5))^2 + (6 - (-6))^2)} = \sqrt{0^2 + (12)^2} = \sqrt{144} = 12
\]

3. **Distance CD**:
\[
\sqrt{((6 - (-5))^2 + (6 - 6)^2)} = \sqrt{(11)^2 + 0^2} = \sqrt{121} = 11
\]

4. **Distance DE**:
\[
\sqrt{((6 - 6)^2 + (1 - 6)^2)} = \sqrt{0^2 + (-5)^2} = \sqrt{25} = 5
\]

5. **Distance EF**:
\[
\sqrt{((2 - 6)^2 + (1 - 1)^2)} = \sqrt{(-4)^2 + 0^2} = \sqrt{16} = 4
\]

6. **Distance FA**:
\[
\sqrt{((2 - 2)^2 + (-6 - 1)^2)} = \sqrt{0^2 + (-7)^2} = \sqrt{49} = 7
\]

Now we can find the total perimeter (P) by adding all the distances:
\[
P = AB + BC + CD + DE + EF + FA = 7 + 12 + 11 + 5 + 4 + 7 = 46
\]

Therefore, the perimeter of the polygon is **46 kilometers**.

The correct response is:
**46 kilometers**.