Question

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

30 units^2

20 units^2

40 units^2

10 units^2

Answer 1

To find the area of the rectangle formed by the coordinates \((-3,1)\), \((-2,-4)\), \((4,-2)\), and \((3,1)\), we first need to identify the length and width of the rectangle.

1. Identify the minimum and maximum x-coordinates:
- The x-coordinates are: \(-3, -2, 4, 3\)
- Minimum x-coordinate: \(-3\)
- Maximum x-coordinate: \(4\)

The length of the rectangle in the x-direction is:
\[
L_x = \text{Maximum x} - \text{Minimum x} = 4 - (-3) = 4 + 3 = 7 \text{ units}
\]

2. Identify the minimum and maximum y-coordinates:
- The y-coordinates are: \(1, -4, -2, 1\)
- Minimum y-coordinate: \(-4\)
- Maximum y-coordinate: \(1\)

The width of the rectangle in the y-direction is:
\[
L_y = \text{Maximum y} - \text{Minimum y} = 1 - (-4) = 1 + 4 = 5 \text{ units}
\]

3. Calculate the area of the rectangle:
\[
\text{Area} = L_x \times L_y = 7 \times 5 = 35 \text{ units}^2
\]

So, the approximate area of the rectangle is **35 units²**. However, it appears that none of the given options (30, 20, 40, or 10 units²) directly match this calculated area. Please double-check the coordinates or options provided.