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

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

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

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

(0, 7)

Answer 1

To find the new coordinates of the endpoints after a 90° clockwise rotation, we can use the transformation rules for rotation in the Cartesian plane. For a point \((x, y)\), a 90° clockwise rotation results in the coordinates \((y, -x)\).

Let's start with the first endpoint of the line segment which is \((0, -3)\):

1. Applying the rotation: \[ (0, -3) \rightarrow (-3, 0) \]

Now, let's do the same for the second endpoint of the line segment which is \((0, -7)\):

2. Applying the rotation: \[ (0, -7) \rightarrow (-7, 0) \]

Based on these calculations, the new endpoints after a 90° clockwise rotation are \((-3, 0)\) and \((-7, 0)\).

From the provided options, the endpoint \((-3, 0)\) matches one of our results.

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