Question

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′(−6,2)
upper Y prime left parenthesis negative 6 comma 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 image of point Y(−2, 6) after a 180° counterclockwise rotation about the origin, we can follow this rule:

A point (x, y) rotated 180° about the origin becomes (-x, -y).

Applying this to point Y(−2, 6):

- The x-coordinate: -(-2) = 2
- The y-coordinate: -(6) = -6

Therefore, the image of point Y after a 180° rotation about the origin is Y′(2, -6).

The correct response is:

Y′(2, −6)