Question

Fill in the steps to find the area of the rectangle. Units are in feet.

A(-4,1)
B(-2,4)
C(4,0)
D(2,-3)



(5 points)
Step 1: Find the ___ of the line that connects C to D and the line that connects ___.

Once these are found, we will ___ these.

The final answer is approximately ___ ___ .

Answer 1

To find the area of the rectangle defined by the points A(-4,1), B(-2,4), C(4,0), and D(2,-3), we can follow the steps outlined below:

**Step 1:** Find the **length** of the line that connects C to D and the line that connects **A to B**.

Once these are found, we will **multiply** these.

The final answer is approximately **___ square feet**.

Now, let's calculate the lengths:

1. **Length of line CD (C(4,0) to D(2,-3))**:
- Using the distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
- \( d_{CD} = \sqrt{(2 - 4)^2 + (-3 - 0)^2} = \sqrt{(-2)^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13} \)

2. **Length of line AB (A(-4,1) to B(-2,4))**:
- Using the distance formula:
- \( d_{AB} = \sqrt{(-2 - (-4))^2 + (4 - 1)^2} = \sqrt{(2)^2 + (3)^2} = \sqrt{4 + 9} = \sqrt{13} \)

Both lengths are \(\sqrt{13}\).

To find the area of the rectangle:

Area = Length × Width = \( \sqrt{13} \times \sqrt{13} = 13 \) square feet.

So, the completed answer is:

The final answer is approximately **13 square feet**.