To find the area of the rectangle formed by the points A(-5,6), B(-2,6), C(-2,1), and D(-5,1), we can start by determining the lengths of the sides of the rectangle.
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Coordinates of the points:
- A(-5, 6) is at the top left.
- B(-2, 6) is at the top right.
- C(-2, 1) is at the bottom right.
- D(-5, 1) is at the bottom left.
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Lengths of the sides:
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Length of AB (horizontal distance between A and B): \[ AB = x_B - x_A = -2 - (-5) = -2 + 5 = 3 \]
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Length of AD (vertical distance between A and D): \[ AD = y_A - y_D = 6 - 1 = 5 \]
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Area of the rectangle: The area \( A \) of a rectangle is given by the formula: \[ A = \text{Length} \times \text{Width} \] Substituting the lengths we found: \[ A = AB \times AD = 3 \times 5 = 15 \]
Thus, the area of the rectangle is \( 15 \) square units.
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