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) Responses Y′(2,−6) upper Y prime left parenthesis 2 comma negative 6 right parenthesis Y′(−6,2) upper Y prime left parenthesis negative 6 comma 2 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 point \( Y' \) after a 180° rotation about the origin, we take the coordinates of point \( Y(-2, 6) \) and apply the rotation transformation.

The formula for rotating a point \( (x, y) \) by 180° about the origin is:

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

Applying this transformation to point \( Y(-2, 6) \):

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

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

Thus, the correct response is:

Y′(2,−6).