Question

Question
Use the image to answer the question.

Parallelogram upper A upper B upper C upper D is graphed on a coordinate plane. The x-axis ranges from negative 6 to 6 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 1.

Use the given coordinates to compute the perimeter of the parallelogram.

(1 point)
Responses

25.2 units
25.2 units

28 units
28 units

26.6 units
26.6 units

13.3 units
13.3 units
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page 17 of 17
Answer
A=(-5,-4),B=(2,-4),C=(4,2),D=(-3,2)
Answered by GPT-4o mini
To calculate the perimeter of a parallelogram, you need to find the lengths of two adjacent sides and then use the following formula:

\[
\text{Perimeter} = 2 \times (length_1 + length_2)
\]

Since the specific coordinates of the points \( A, B, C, D \) were not provided, I can’t calculate the lengths directly. However, you can find the lengths of the sides by using the distance formula between the points that define two adjacent sides of the parallelogram. The distance formula is:

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

1. Choose two adjacent vertices (for example, \( A \) and \( B \)).
2. Calculate the length of side \( AB \) using the distance formula.
3. Do the same for another adjacent side (for example, \( AB \) and \( AD \)).
4. Add the two lengths together and multiply by 2 to find the perimeter.

If you provide the coordinates of points \( A, B, C, \) and \( D \), I can help you with the exact calculations. Otherwise, please use the steps outlined to find the perimeter.
Answered by GPT-4o mini
Given the coordinates of the parallelogram \( A(-5,-4) \), \( B(2,-4) \), \( C(4,2) \), and \( D(-3,2) \), we can calculate the lengths of two adjacent sides and then find the perimeter.

### Step 1: Calculate the lengths of sides \( AB \) and \( AD \).

#### Length of side \( AB \):
Using the distance formula:

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

Substituting in the coordinates of points \( A \) and \( B \):

\[
d_{AB} = \sqrt{(2 - (-5))^2 + (-4 - (-4))^2}
\]
\[
d_{AB} = \sqrt{(2 + 5)^2 + (0)^2} = \sqrt{7^2 + 0} = \sqrt{49} = 7
\]

#### Length of side \( AD \):
Now using points \( A \) and \( D \):

\[
d_{AD} = \sqrt{(-3 - (-5))^2 + (2 - (-4))^2}
\]
\[
d_{AD} = \sqrt{(-3 + 5)^2 + (2 + 4)^2}
\]
\[
d_{AD} = \sqrt{(2)^2 + (6)^2} = \sqrt{4 + 36} = \sqrt{40} \approx 6.32
\]

### Step 2: Calculate the perimeter of the parallelogram.

The perimeter formula for a parallelogram is:

\[
\text{Perimeter} = 2 \times (length_1 + length_2)
\]

Where \( length_1 = AB \) and \( length_2 = AD \):

\[
\text{Perimeter} = 2 \times (7 + 6.32) = 2 \times 13.32 \approx 26.64
\]

### Conclusion:
The perimeter of the parallelogram \( ABCD \) is approximately \( 26.6 \) units.

The most accurate answer choice from the given options is:
**26.6 units**.