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

Answer 1

To rotate a point 90 degrees clockwise around the origin, we can use the transformation formula:

\[ (x, y) \rightarrow (y, -x) \]

Let's apply this transformation to each endpoint of the line segment.

1. For the endpoint \((0, -3)\):

   • After rotation, the new coordinates will be: \[ (0, -3) \rightarrow (-3, -0) = (-3, 0) \]

2. For the endpoint \((0, -7)\):

   • After rotation, the new coordinates will be: \[ (0, -7) \rightarrow (-7, 0) \]

Thus, after rotating the line segment with endpoints \((0, -3)\) and \((0, -7)\) 90 degrees clockwise, the new endpoints of the rotated segment are \((-3, 0)\) and \((-7, 0)\).

Therefore, one of the endpoints of the rotated segment is \((-3, 0)\) (and the other is \((-7, 0)\)).