To find the perimeter of the rectangle, we first need to determine the lengths of its sides.
The vertices of the rectangle are:
- A(-7, -2)
- B(-3, -2)
- C(-3, -5)
- D(-7, -5)
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Calculate the length of the horizontal sides (AB and CD):
- The length can be found by taking the difference in the x-coordinates of points A and B (or C and D): \[ |x_2 - x_1| = |-3 - (-7)| = |-3 + 7| = |4| = 4 \text{ units} \]
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Calculate the length of the vertical sides (AD and BC):
- The length can be found by taking the difference in the y-coordinates of points A and D (or B and C): \[ |y_2 - y_1| = |-5 - (-2)| = |-5 + 2| = |-3| = 3 \text{ units} \]
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Calculate the perimeter of the rectangle:
- The perimeter \( P \) of a rectangle is given by the formula: \[ P = 2 \times (\text{length} + \text{width}) \] where length is 4 units and width is 3 units. \[ P = 2 \times (4 + 3) = 2 \times 7 = 14 \text{ units} \]
Thus, the perimeter of the rectangle is 14 units.