To determine the coordinates of rectangle ABCD, we have:
- Point A: \((-3, -2)\)
- Point B: \((4, -2)\)
- Point C: \((4, 1)\)
- Point D: \((-3, 1)\)
Next, we can verify the shape is a rectangle and calculate its area.
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Calculate the lengths of the sides:
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Length of side \(AB\) (horizontal side) can be calculated as: \[ AB = x_B - x_A = 4 - (-3) = 4 + 3 = 7 \]
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Length of side \(AD\) (vertical side) can be calculated as: \[ AD = y_D - y_A = 1 - (-2) = 1 + 2 = 3 \]
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Calculate the area of the rectangle: The area \(A\) of the rectangle can be calculated using the formula: \[ A = \text{length} \times \text{width} = AB \times AD \] Substituting in the values we found: \[ A = 7 \times 3 = 21 \]
The coordinates of rectangle ABCD are confirmed, and the area of the rectangle is \(21\) square units.
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