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)
upper Y prime left parenthesis negative 6 comma 2 right parenthesis

Answer 1

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

\[ (x', y') = (-x, -y) \]

Starting with the coordinates of point \( Y(-2, 6) \):

• The new x-coordinate will be: \(-(-2) = 2\)
• The new y-coordinate will be: \(-6\)

So, the coordinates of point \( Y' \) after the rotation will be:

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

Therefore, the answer is:

Y′(2,−6)