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

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

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

(0, 3)

Answer 1

To determine the rotated position of a point after a 90° clockwise rotation, we can use the rotation formula for a point \((x, y)\):

1. For a 90° clockwise rotation, the new coordinates \((x', y')\) can be calculated as: \[ (x', y') = (y, -x) \]

Let's find the rotated positions of the endpoints of the line segment with endpoints \((0, -3)\) and \((0, -7)\).

1. Rotating the first endpoint \((0, -3)\): \[ (x', y') = (-3, -0) = (-3, 0) \]

2. Rotating the second endpoint \((0, -7)\): \[ (x', y') = (-7, -0) = (-7, 0) \]

So, the first endpoint after the rotation is \((-3, 0)\) and the second endpoint is \((-7, 0)\).

Since the question asks for one of the endpoints after rotation, the first endpoint \((-3, 0)\) is a valid response.

Thus, the answer is: \[ \boxed{(-3, 0)} \]