To find the perimeter of rectangle LMNO with vertices \( L(-2, -1) \), \( M(-5, -1) \), \( N(-5, -6) \), and \( O(-2, -6) \), we first need to determine the lengths of the sides.
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Calculate the length of side LM: Since points L and M have the same y-coordinate, the distance between them is simply the difference in their x-coordinates: \[ LM = |x_M - x_L| = |-5 - (-2)| = |-5 + 2| = |-3| = 3 \text{ units} \]
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Calculate the length of side LN: Similarly, points L and N have the same x-coordinate, so we find the distance by taking the difference in their y-coordinates: \[ LN = |y_N - y_L| = |-6 - (-1)| = |-6 + 1| = |-5| = 5 \text{ units} \]
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Calculate the perimeter of rectangle LMNO: The perimeter \( P \) of a rectangle is given by the formula: \[ P = 2 \times (length + width) = 2 \times (LM + LN) \] Substituting the values we found: \[ P = 2 \times (3 + 5) = 2 \times 8 = 16 \text{ units} \]
Thus, the perimeter of rectangle LMNO is 16 units.