Demonstrating the properties of rotations, if a line segment with endpoints and is rotated

Question

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: \[ \boxed{(-3, 0)} \]