To find the length of the line segment after it has been rotated, we first need to determine the original length of the segment between the points \( (0, 4) \) and \( (3, 4) \).
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Calculate the original length: The length of a line segment between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the endpoints \((0, 4)\) and \((3, 4)\):
\[ d = \sqrt{(3 - 0)^2 + (4 - 4)^2} = \sqrt{3^2 + 0^2} = \sqrt{9} = 3 \]
So, the original length of the line segment is \(3\).
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Determine the effect of rotation: When the segment is rotated 270° clockwise, it does not change the length of the segment. Rotating a geometric figure does not alter its dimensions; it only changes its orientation.
Hence, after rotating the segment 270° clockwise, the length of the segment remains:
\[ \text{Length of the segment} = 3 \]
Therefore, the length of the segment after rotation will still be 3.