Question

Demonstrating the properties of rotations, if a line segment with endpoints and is rotated
clockwise, what is an endpoint of this rotated segment? (1 point)
(0, −3) (0, −7)
90°
(0, 7)
(3, 0)
(0, 3)
(−3, 0)

Answer 1

To find the coordinates of the endpoints of the line segment \((0, -3)\) and \((0, -7)\) when rotated clockwise by \(90^\circ\), we will apply the transformation for rotation.

The general rule for rotating a point \((x, y)\) by \(90^\circ\) clockwise around the origin is given by:
\[
(x, y) \rightarrow (y, -x)
\]

Now, we will apply this transformation to both endpoints of the segment.

1. For the point \((0, -3)\):
\[
(0, -3) \rightarrow (-3, 0)
\]

2. For the point \((0, -7)\):
\[
(0, -7) \rightarrow (-7, 0)
\]

So after the rotation, the new endpoints of the line segment are \((-3, 0)\) and \((-7, 0)\).

Therefore, one of the endpoints of the rotated segment is \((-3, 0)\).

Hence, the answer is:
\[
\boxed{(-3, 0)}
\]