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, 7)
left parenthesis 0 comma 7 right parenthesis

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

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

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

Answer 1

To determine the endpoint of the line segment after a 90° clockwise rotation, we first need to identify the original endpoints of the line segment:

1. The first endpoint is (0, -3).
2. The second endpoint is (0, -7).

Let's rotate each endpoint 90° clockwise around the origin (0,0). The formula for rotating a point (x, y) 90° clockwise is given by:

\[ (x', y') = (y, -x) \]

Rotate the first endpoint (0, -3):

Using the formula:

• Original point: (x, y) = (0, -3)
• After rotation: \[ (x', y') = (-3, 0) \]

Rotate the second endpoint (0, -7):

Using the formula:

• Original point: (x, y) = (0, -7)
• After rotation: \[ (x', y') = (-7, 0) \]

Summary of results:

• The first endpoint (0, -3) rotates to (-3, 0).
• The second endpoint (0, -7) rotates to (-7, 0).

To answer the question, one of the endpoints that results from the rotation of this segment is:

(−3, 0)

So, the correct response is:

\((−3, 0)\)