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