Question

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?(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 a point (x, y) 90° clockwise around the origin, the new coordinates (x', y') can be given by the transformation:

\[ (x', y') = (y, -x) \]

We are given the endpoints of the line segment: (0, −3) and (0, −7).

1. Rotating the first endpoint (0, -3):
   • x = 0
   • y = -3

Using our transformation: \[ (x', y') = (y, -x) = (-3, -0) = (-3, 0) \]

So, the first rotated endpoint is (-3, 0).

2. Rotating the second endpoint (0, -7):
   • x = 0
   • y = -7

Using our transformation: \[ (x', y') = (y, -x) = (-7, -0) = (-7, 0) \]

So, the second rotated endpoint is (-7, 0).

Among the response options offered:

• (0, 3)
• (−3, 0)
• (0, 7)
• (3, 0)

The correct response for one of the rotated endpoints is: (−3, 0).