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′(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

Answer 1

To find the image of point \( Y(-2, 6) \) after a \( 180^\circ \) counterclockwise rotation about the origin, we can use the following transformation rule:

For a point \( (x, y) \), the coordinates after a \( 180^\circ \) rotation about the origin will be \( (-x, -y) \).

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

1. Negate the x-coordinate:
\[
-(-2) = 2
\]

2. Negate the y-coordinate:
\[
-(6) = -6
\]

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

So the correct response is:
\[
Y'(2, -6)
\]