To find the length of the segment with endpoints (0, 4) and (3, 4), we first determine its length using the distance formula:
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For the points \((0, 4)\) and \((3, 4)\):
- \(x_1 = 0\), \(y_1 = 4\)
- \(x_2 = 3\), \(y_2 = 4\)
Plugging in the values:
\[ d = \sqrt{(3 - 0)^2 + (4 - 4)^2} = \sqrt{(3)^2 + (0)^2} = \sqrt{9} = 3 \]
Now, regarding the second part of your question about the length after the segment is rotated clockwise:
The length of the segment remains the same regardless of how it is rotated. Rotating a line segment moves its endpoints, but does not change the distance between them.
Therefore, after the segment is rotated clockwise, the length of the segment will still be:
\[ \text{Length} = 3 \]
The length of the segment remains 3 units even after rotation.