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

Answer 1

To find the endpoint of the line segment after a 90° clockwise rotation, we can follow these steps:

1. Identify the original endpoints of the line segment. The endpoints are:

   • A(0, -3)
   • B(0, -7)

2. To rotate a point (x, y) 90° clockwise around the origin, we can use the following transformation: \[ (x, y) \to (y, -x) \]

3. Let's rotate each endpoint:

   • For A(0, -3): \[ (0, -3) \to (-3, 0) \]

   • For B(0, -7): \[ (0, -7) \to (-7, 0) \]

So after the 90° clockwise rotation, the new endpoints of the segment are:

• A'(-3, 0)
• B'(-7, 0)

Among the answers provided, the one that matches is \((-3, 0)\).

Thus, the answer is: \[ \text{(−3, 0)} \]