To find the perimeter of a rectangle, we typically need to identify the lengths of its sides. However, the coordinates provided—(0,0), (4,4), (5,3), and (1,-1)—do not form a rectangle since a rectangle's opposite sides must be parallel and equal in length.
Let's calculate the lengths of the sides connecting these points:
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Distance between (0,0) and (4,4): \[ d = \sqrt{(4-0)^2 + (4-0)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \approx 5.7 \]
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Distance between (4,4) and (5,3): \[ d = \sqrt{(5-4)^2 + (3-4)^2} = \sqrt{1 + 1} = \sqrt{2} \approx 1.4 \]
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Distance between (5,3) and (1,-1): \[ d = \sqrt{(1-5)^2 + (-1-3)^2} = \sqrt{(-4)^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \approx 5.7 \]
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Distance between (1,-1) and (0,0): \[ d = \sqrt{(0-1)^2 + (0+1)^2} = \sqrt{1 + 1} = \sqrt{2} \approx 1.4 \]
Now we can sum these distances to find the total length of the polygon:
\[ \text{Total length} = 4\sqrt{2} + \sqrt{2} + 4\sqrt{2} + \sqrt{2} = 6\sqrt{2} + 2\sqrt{2} = 8\sqrt{2} \]
Calculating \(8\sqrt{2}\): \[ 8\sqrt{2} \approx 8 \times 1.414 = 11.3 \]
Thus, the total perimeter of the shape formed by these points is approximately 11.3 when rounded to the nearest tenth.
However, please note that since these points do not form a rectangle, this is merely the total length of the polygon connecting these points. If you specifically want the rectangle, we can validate with pairs of points to see if a rectangle configuration is possible here, but based on provided coordinates they do not directly indicate a rectangle.