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 negative 3 comma 0 right parenthesis

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

(0, 3)

Answer 1

To rotate the line segment with endpoints (0, -3) and (0, -7) 90° clockwise, we can use the rotation formula for clockwise rotation about the origin, which is:

\[ (x, y) \rightarrow (y, -x) \]

Let's apply this to each endpoint:

1. For the point (0, -3):

\[ (0, -3) \rightarrow (-3, 0) \]

2. For the point (0, -7):

\[ (0, -7) \rightarrow (-7, 0) \]

So, after rotating 90° clockwise, the endpoints of the segment are (-3, 0) and (-7, 0).

One of the endpoints after rotation is:

\[ \text{Answer: } (-3, 0) \]