To find the perimeter of rectangle ABCD with vertices A(-8, 3), B(-1, 3), C(-1, -6), and D(-8, -6), we need to first calculate the lengths of the sides.
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Calculate the length of AB: Points A and B have the same y-coordinate (3). Thus, the length of side AB can be calculated as the difference in x-coordinates:
\[ AB = |x_B - x_A| = |-1 - (-8)| = |-1 + 8| = |7| = 7 \text{ units} \]
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Calculate the length of AD: Points A and D have the same x-coordinate (-8). Thus, the length of side AD can be calculated as the difference in y-coordinates:
\[ AD = |y_D - y_A| = |-6 - 3| = |-9| = 9 \text{ units} \]
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The perimeter (P) of the rectangle is given by the formula: \[ P = 2 \times (AB + AD) \] Substituting the lengths we calculated: \[ P = 2 \times (7 + 9) = 2 \times 16 = 32 \text{ units} \]
Therefore, the perimeter of rectangle ABCD is 32 units.