A segment has endpoints X(−10,0) and Y(−2,6). Consider its image after a 180° (counterclockwise) rotation about the origin. Select the coordinates of Y′.(1 point)

Question

Responses

Y′(6,−2)
upper Y prime left parenthesis 6 comma negative 2 right parenthesis

Y′(2,−6)
upper Y prime left parenthesis 2 comma negative 6 right parenthesis

Y′(−2,−6)
upper Y prime left parenthesis negative 2 comma negative 6 right parenthesis

Y′(−6,2)

Answer 1

To find the coordinates of the image \( Y' \) after a 180° counterclockwise rotation about the origin, we can use the following transformation:

For a point \( (x, y) \), a 180° rotation about the origin transforms it to \( (-x, -y) \).

The coordinates of point \( Y \) are \( (-2, 6) \).

After applying the transformation:

\[ Y' = (-(-2), -6) = (2, -6) \]

Thus, the coordinates of \( Y' \) are \( (2, -6) \).

Therefore, the correct response is:

Y′(2,−6).