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

Answer 1

To find the image of point Y(−2,6) after a 180° counterclockwise rotation about the origin, you can apply the following transformation:

For a 180° rotation about the origin, the new coordinates (x', y') of a point (x, y) are given by:

• x' = -x
• y' = -y

Applying this to point Y(−2, 6):

1. x' = -(-2) = 2
2. y' = -6

So the new coordinates for Y′ after the rotation will be Y′(2, -6).

Thus, the correct choice is: Y′(2,−6) (Y prime left parenthesis 2, negative 6 right parenthesis).