Demonstrating the properties of rotations, if a line segment with endpoints (0,−3)

Question

and (0,−7)
is rotated 90°
clockwise, what is an endpoint of this rotated segment?(1 point)
Responses

(0, 3)
left parenthesis 0 comma 3 right parenthesis

(−3, 0)
left parenthesis negative 3 comma 0 right parenthesis

(0, 7)
left parenthesis 0 comma 7 right parenthesis

(3, 0)

Answer 1

To rotate the line segment with endpoints \( (0, -3) \) and \( (0, -7) \) 90° clockwise, we will first analyze the endpoint that we will rotate, \( (0, -3) \).

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

2. Apply this transformation to the point \( (0, -3) \): \[ (0, -3) \rightarrow (-3, 0) \]

Thus, the endpoint \( (0, -3) \) when rotated 90° clockwise becomes \( (-3, 0) \).

We can also apply the same transformation to the other endpoint \( (0, -7) \): \[ (0, -7) \rightarrow (-7, 0) \]

However, the question specifically asks for an endpoint of the rotated segment (which includes the transformed endpoint of \( (0, -3) \)), therefore the answer is:

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