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, 3) left parenthesis 0 comma 3 right parenthesis (−3, 0) left parenthesis negative 3 comma 0 right parenthesis (0, 7) left parenthesis 0 comma 7 right parenthesis (3, 0)

Answer 1

To rotate a point (x, y) 90° clockwise around the origin, the new coordinates (x', y') can be given by the transformation:

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

We are given the endpoints of the line segment: (0, −3) and (0, −7).

1. **Rotating the first endpoint (0, -3)**:
- x = 0
- y = -3

Using our transformation:
\[
(x', y') = (y, -x) = (-3, -0) = (-3, 0)
\]

So, the first rotated endpoint is **(-3, 0)**.

2. **Rotating the second endpoint (0, -7)**:
- x = 0
- y = -7

Using our transformation:
\[
(x', y') = (y, -x) = (-7, -0) = (-7, 0)
\]

So, the second rotated endpoint is **(-7, 0)**.

Among the response options offered:
- (0, 3)
- (−3, 0)
- (0, 7)
- (3, 0)

The correct response for one of the rotated endpoints is: **(−3, 0)**.