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

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

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

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

(0, 3)

Answer 1

To rotate a point around the origin (0, 0) by 90° clockwise, you can use the following transformation:

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

Now, we can determine the endpoints of the line segment given, which are (0, -3) and (0, -7):

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

   Applying the transformation: \[ (0, -3) \rightarrow (-3, 0) \]

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

   Applying the transformation: \[ (0, -7) \rightarrow (-7, 0) \]

Now, since the question asks for just one of the rotated endpoints, and we are given multiple-choice options, the correct rotated endpoint for the first point (0, -3) is:

\((-3, 0)\).

Thus, the answer is:

(−3, 0)