Question

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, 7)
left parenthesis 0 comma 7 right parenthesis

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

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

(3, 0)

Answer 1

To find the endpoint of the line segment (0, -3) and (0, -7) after a 90° clockwise rotation, we need to follow these steps:

1. Identify the endpoints: The original endpoints are (0, -3) and (0, -7).

2. Rotate (0, -3):

   • The formula for rotating a point \( (x, y) \) 90° clockwise around the origin is \( (y, -x) \).
   • For point (0, -3):
     • \( x = 0 \) and \( y = -3 \).
     • After rotation:
       • New coordinates = (-3, 0).

3. Rotate (0, -7):

   • For point (0, -7):
     • \( x = 0 \) and \( y = -7 \).
     • After rotation:
       • New coordinates = (-7, 0).

Now we have the rotated endpoints:

• (0, -3) rotates to (-3, 0)
• (0, -7) rotates to (-7, 0)

The question asks for one of the rotated endpoints. Among the options provided, the rotated endpoint (0, -3) corresponds to (-3, 0).

Therefore, the answer is: (−3, 0).