To find the area of the rectangle formed by the given coordinates, we first need to identify the coordinates of the rectangle's corners. The points provided are:
- (3, 3)
- (0, 0)
- (7, -1)
- (4, -4)
Now we will find the minimum and maximum x-coordinates and the minimum and maximum y-coordinates to determine the corners of the rectangle:
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The x-coordinates are: 3, 0, 7, 4
- Minimum x-coordinate: 0
- Maximum x-coordinate: 7
-
The y-coordinates are: 3, 0, -1, -4
- Minimum y-coordinate: -4
- Maximum y-coordinate: 3
So, the corners of the rectangle can be defined by the coordinates of the rectangle's boundaries:
- Bottom left corner: (0, -4)
- Top right corner: (7, 3)
To compute the area of the rectangle, we can use the formula: \[ \text{Area} = \text{width} \times \text{height} \]
Width (difference in x-coordinates): \[ \text{Width} = x_{\text{max}} - x_{\text{min}} = 7 - 0 = 7 \]
Height (difference in y-coordinates): \[ \text{Height} = y_{\text{max}} - y_{\text{min}} = 3 - (-4) = 3 + 4 = 7 \]
Now, we can calculate the area: \[ \text{Area} = \text{Width} \times \text{Height} = 7 \times 7 = 49 \]
Thus, the exact area of the rectangle is \( \boxed{49} \).
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