Question

Use The coordinates (-3,-1),(-2,-4),(4,-2) and (3,1) to compute to the approximate area of the rectangle

Answer 1

To find the area of a rectangle given the coordinates, we need to identify two opposite corners (vertices) of the rectangle. The area can be calculated using the formula:

\[
\text{Area} = \text{length} \times \text{width}
\]

First, let's identify the minimum and maximum x and y values from the given coordinates:

- Points:
1. (-3, -1)
2. (-2, -4)
3. (4, -2)
4. (3, 1)

### Step 1: Determine the min/max coordinates
- For x-coordinates, we have:
- Minimum x = -3 (from point (-3, -1))
- Maximum x = 4 (from point (4, -2))

- For y-coordinates, we have:
- Minimum y = -4 (from point (-2, -4))
- Maximum y = 1 (from point (3, 1))

### Step 2: Calculate the length and width
- Length of the rectangle (along the x-axis):
\[
\text{Length} = \text{Maximum x} - \text{Minimum x} = 4 - (-3) = 4 + 3 = 7
\]

- Width of the rectangle (along the y-axis):
\[
\text{Width} = \text{Maximum y} - \text{Minimum y} = 1 - (-4) = 1 + 4 = 5
\]

### Step 3: Calculate the area
Now we can calculate the area of the rectangle:
\[
\text{Area} = \text{Length} \times \text{Width} = 7 \times 5 = 35
\]

Therefore, the approximate area of the rectangle formed by the given points is **35 square units.**