Use the coordinates to compute the approximate area of the rectangle. Round to the nearest whole number. (1 point) Responses 4 4 32 32 6 6 8

Answer 1

To compute the area of a rectangle, you need the length and width. Based on the coordinates given (though not specified in your question), it seems like you might have pairs of coordinates that define the corners of the rectangle.

If the coordinates are:

• Bottom-left corner at (x1, y1)
• Top-right corner at (x2, y2)

Then, the length (L) and width (W) can be computed as follows:

• Length = |x2 - x1|
• Width = |y2 - y1|

The area (A) of the rectangle can then be calculated with the formula: \[ A = L \times W \]

If we assume the coordinates are:

• (4, 4) and (8, 6) for example.

Calculating length and width:

• Length: |8 - 4| = 4
• Width: |6 - 4| = 2

Then the area would be: \[ A = 4 \times 2 = 8 \]

Since we do not have specific coordinates provided, please use the input coordinates and apply the above method to compute the area.

If you want a specific response based on the numbers 4, 32, 6, or 8, without more details, it’s difficult to provide a numerical answer. If you could clarify with the specific coordinates, I could then help calculate the area more accurately.

Answer 2

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

Answer 3

To find the area of the rectangle formed by the points \( A (1,1) \), \( B (0,2) \), \( C (2,4) \), and \( D (3,3) \), we first need to identify which points are opposite vertices of the rectangle.

Let's examine the coordinates:

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

We can find the distances between points to determine the lengths of the sides.

Calculating the distances:

1. Distance between \( A(1, 1) \) and \( B(0, 2) \): \[ d(AB) = \sqrt{(1 - 0)^2 + (1 - 2)^2} = \sqrt{1^2 + (-1)^2} = \sqrt{1 + 1} = \sqrt{2} \approx 1.414 \]

2. Distance between \( A(1, 1) \) and \( C(2, 4) \): \[ d(AC) = \sqrt{(1 - 2)^2 + (1 - 4)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.162 \]

3. Distance between \( A(1, 1) \) and \( D(3, 3) \): \[ d(AD) = \sqrt{(1 - 3)^2 + (1 - 3)^2} = \sqrt{(-2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.828 \]

4. Distance between \( B(0, 2) \) and \( C(2, 4) \): \[ d(BC) = \sqrt{(0 - 2)^2 + (2 - 4)^2} = \sqrt{(-2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.828 \]

5. Distance between \( B(0, 2) \) and \( D(3, 3) \): \[ d(BD) = \sqrt{(0 - 3)^2 + (2 - 3)^2} = \sqrt{(-3)^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10} \approx 3.162 \]

6. Distance between \( C(2, 4) \) and \( D(3, 3) \): \[ d(CD) = \sqrt{(2 - 3)^2 + (4 - 3)^2} = \sqrt{(-1)^2 + (1)^2} = \sqrt{1 + 1} = \sqrt{2} \approx 1.414 \]

From this information, we can assess the arrangement of the points. They do not form a typical rectangle due to the angles formed by them, as the lengths calculated do not indicate opposite equal sides.

If you want to calculate the area of the quadrilateral formed by these points, you can use the Shoelace formula:

\[ \text{Area} = \frac{1}{2} \left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1) \right| \]

Assigning the coordinates:

• \( (x_1, y_1) = (1, 1) \)
• \( (x_2, y_2) = (0, 2) \)
• \( (x_3, y_3) = (2, 4) \)
• \( (x_4, y_4) = (3, 3) \)

Now, substituting into the formula:

\[ \text{Area} = \frac{1}{2} \left| 1 \cdot 2 + 0 \cdot 4 + 2 \cdot 3 + 3 \cdot 1 - (1 \cdot 0 + 2 \cdot 2 + 4 \cdot 3 + 3 \cdot 1) \right| \]

Calculating:

\[ = \frac{1}{2} \left| 2 + 0 + 6 + 3 - (0 + 4 + 12 + 3) \right| \] \[ = \frac{1}{2} \left| 11 - 19 \right| \] \[ = \frac{1}{2} \left| -8 \right| = 4 \]

Thus, the approximate area of the quadrilateral formed by the points is 4 square units.