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)

Question

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 $Y^{\prime }$ after the rotation are $(2,-6)$.

So the correct response is: $$Y^{\prime }(2,-6)$$