Question

Rotations Practice
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Question
If a segment has endpoints (0, 4)
and (3, 4)
, how long will the segment be after it is rotated 270°
clockwise?(1 point)
units

Answer 1

To find the length of the segment after rotation, we first need to determine the initial length of the segment defined by the endpoints (0, 4) and (3, 4).

1. **Calculate the length of the segment.**
Since both endpoints have the same y-coordinate (4), the segment is horizontal. The distance can be found using the distance formula or simply by taking the difference of the x-coordinates:

\[
\text{Length} = x_2 - x_1 = 3 - 0 = 3 \text{ units}
\]

2. **Determine the effect of the 270° clockwise rotation.**
When we rotate a point (x, y) clockwise by 270°, the new coordinates (x', y') can be determined with the formula:

\[
(x', y') = (y, -x)
\]

Let's compute the new coordinates for each endpoint after the rotation.

- For point (0, 4):
- After 270° rotation:
\[
(4, -0) = (4, 0)
\]

- For point (3, 4):
- After 270° rotation:
\[
(4, -3)
\]

3. **Calculate the length of the rotated segment.**
Now, the new endpoints are (4, 0) and (4, -3). Since both points now have the same x-coordinate (4), this segment is vertical. The distance can be calculated by taking the difference of the y-coordinates:

\[
\text{Length} = y_1 - y_2 = 0 - (-3) = 3 \text{ units}
\]

In conclusion, the length of the segment after it is rotated 270° clockwise remains **3 units**.