To find the area of the rectangle defined by the given coordinates (0,0), (3,3), (7,-1), and (4,-4), we first need to verify whether these points describe a rectangle and identify the lengths of its sides.
Step 1: Identify the vertices
We have the coordinates A(0,0), B(3,3), C(7,-1), and D(4,-4). To describe a rectangle, the sides must be parallel to the x-axis and y-axis.
Step 2: Evaluate points
The points aren't clearly arranged, so we'll determine the maximum and minimum x and y coordinates to see if they can isolate the extents of a rectangle.
- The x-coordinates are: 0, 3, 7, 4
- The y-coordinates are: 0, 3, -1, -4
Step 3: Find the bounds
- Minimum x-coordinate: \( \min(0, 3, 7, 4) = 0 \)
- Maximum x-coordinate: \( \max(0, 3, 7, 4) = 7 \)
- Minimum y-coordinate: \( \min(0, 3, -1, -4) = -4 \)
- Maximum y-coordinate: \( \max(0, 3, -1, -4) = 3 \)
Step 4: Calculate the width and height
The width of the rectangle is the difference between the maximum and minimum x-coordinates, and the height is the difference between the maximum and minimum y-coordinates.
- Width: \( 7 - 0 = 7 \)
- Height: \( 3 - (-4) = 3 - (-4) = 3 + 4 = 7 \)
Step 5: Calculate the area
The area \( A \) of a rectangle is given by:
\[ A = \text{Width} \times \text{Height} \]
Substituting in the values we found:
\[ A = 7 \times 7 = 49 \]
However, the maximum area we calculated does not correspond to any of the given answer choices. Thus it suggests that the four points do not form a rectangle in order.
Conclusion
Based on computation and analysis, conclusions indicate that the points do not actually delineate a proper rectangle due to non-parallel side orientation. Since none of the options (A, B, C, D) were reached, please check the coordinates or whether we should interpret them in a quadrilateral versus strictly rectangular form. Based on a standard recognition of geometric shape constraints, we wouldn’t classify this set as rectangular correctly.
Given the coordinates do not yield valid calculations, request for re-evaluation or verification of input points could also be advised.
Correct Area: Invalid as Rectangle (evaluated space configurations suggest rounding asynchronously) thus offer request to re-check configuration assignments.
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