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 3 comma 0 right parenthesis

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

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

(0, 7)

Answer 1

To find the new endpoints of the line segment after a 90° clockwise rotation, we will first identify the original endpoints and then apply the rotation to each point.

The original endpoints are \( (0, -3) \) and \( (0, -7) \).

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

Let's rotate each endpoint:

1. Rotating (0, -3): \[ (0, -3) \to (-3, 0) \]

2. Rotating (0, -7): \[ (0, -7) \to (-7, 0) \]

Thus, after rotating, the new endpoints are \( (-3, 0) \) and \( (-7, 0) \).

Among the provided options, the answer: \[ (-3, 0) \text{ (left parenthesis negative 3 comma 0 right parenthesis)} \]

is one of the endpoints of the rotated segment.