To find the perimeter of the mirror framed by the coordinates A(−3,4), B(4,4), C(4,1), and D(−3,1), we first need to determine the lengths of the sides of the rectangle formed by these points.
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Identify the points:
- A(−3,4)
- B(4,4)
- C(4,1)
- D(−3,1)
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Calculate the lengths of the sides:
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The distance between points A and B: \[ AB = |x_B - x_A| = |4 - (-3)| = |4 + 3| = 7 \text{ feet} \]
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The distance between points B and C: \[ BC = |y_C - y_B| = |1 - 4| = |1 - 4| = 3 \text{ feet} \]
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The distance between points C and D: \[ CD = |x_D - x_C| = |-3 - 4| = |-3 - 4| = 7 \text{ feet} \]
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The distance between points D and A: \[ DA = |y_A - y_D| = |4 - 1| = |4 - 1| = 3 \text{ feet} \]
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Calculate the perimeter: The perimeter \( P \) of the rectangle can be calculated using the formula: \[ P = 2(AB + BC) = 2(7 + 3) = 2 \times 10 = 20 \text{ feet} \]
Therefore, the perimeter of the mirror is 20 feet. Layan needs to buy a frame that is 20 feet long.