To compute the perimeter of the trapezoid formed by the coordinates (0,0), (0,5), (1,3), and (4,3), we'll first visualize the figure and then calculate the lengths of each side. The trapezoid has a vertical side and two horizontal sides.
The vertices are:
- A (0, 0)
- B (0, 5)
- C (4, 3)
- D (1, 3)
Now, we will find the lengths of sides AB, BC, CD, and DA using the distance formula:
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Length AB: \[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(0 - 0)^2 + (5 - 0)^2} = \sqrt{0 + 25} = \sqrt{25} = 5 \]
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Length BC: \[ BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(4 - 0)^2 + (3 - 5)^2} = \sqrt{(4)^2 + (-2)^2} = \sqrt{16 + 4} = \sqrt{20} \] \[ BC \approx 4.5 \quad \text{(to the nearest tenth)} \]
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Length CD: \[ CD = \sqrt{(1 - 4)^2 + (3 - 3)^2} = \sqrt{(-3)^2 + 0^2} = \sqrt{9} = 3 \]
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Length DA: \[ DA = \sqrt{(0 - 1)^2 + (0 - 3)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \] \[ DA \approx 3.2 \quad \text{(to the nearest tenth)} \]
Now we can compute the perimeter \( P \) of the trapezoid: \[ P = AB + BC + CD + DA \] \[ P = 5 + 4.5 + 3 + 3.2 \] \[ P \approx 15.7 \quad \text{(to the nearest tenth)} \]
Thus, the perimeter of the trapezoid is approximately 15.7 units.