To analyze the rectangle defined by the points \( A(-6,-2) \), \( B(-2,-2) \), \( C(-2,-5) \), and \( D(-6,-5) \), we can verify the properties of the rectangle and calculate its dimensions.
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Vertices:
- A: \((-6, -2)\)
- B: \((-2, -2)\)
- C: \((-2, -5)\)
- D: \((-6, -5)\)
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side lengths:
- The length of side \( AB \) (horizontal length) can be calculated as: \[ AB = |-2 - (-6)| = |-2 + 6| = |4| = 4 \]
- The length of side \( AD \) (vertical length) can be calculated as: \[ AD = |-5 - (-2)| = |-5 + 2| = |-3| = 3 \]
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Area: The area \( A \) of the rectangle is given by the product of its lengths: \[ A = AB \times AD = 4 \times 3 = 12 \]
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Perimeter: The perimeter \( P \) of the rectangle is given by the formula: \[ P = 2(AB + AD) = 2(4 + 3) = 2 \times 7 = 14 \]
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Coordinates and characteristics:
- The rectangle has vertical sides (AD and BC) and horizontal sides (AB and CD).
- The opposite sides are equal, confirming it is indeed a rectangle.
So, the dimensions of the rectangle are:
- Length: 4
- Width: 3
- Area: 12
- Perimeter: 14
The rectangle is positioned in the coordinate plane with \( A \) and \( B \) on the same horizontal line at \( y = -2 \), and \( C \) and \( D \) on the same horizontal line at \( y = -5 \).
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