If a segment has endpoints (0, 4)

Question

(
0
,

4
)
and (3, 4)
(
3
,

4
)
, how long will the segment be after it is rotated 270°
270
°
clockwise?(1 point)
units

Answer 1

To find the length of the segment after it's rotated 270° clockwise, we start by determining the length of the segment before rotation.

The endpoints of the segment are \((0, 4)\) and \((3, 4)\). The length of the segment can be calculated using the distance formula:

\[ \text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates of the endpoints:

\[ \text{Length} = \sqrt{(3 - 0)^2 + (4 - 4)^2} = \sqrt{(3)^2 + (0)^2} = \sqrt{9 + 0} = \sqrt{9} = 3 \]

Now, when we rotate the segment 270° clockwise, the length of the segment remains unchanged. Rotating a line segment does not alter its length; it only changes its orientation in the coordinate plane.

Thus, after rotation, the length of the segment is still:

\[ \boxed{3} \text{ units} \]