A segment has endpoints X(-10,0) and Y(-2,6). Consider its image after a 180 degree ( counterclockwise) rotation about the origin. Select the coordinates of Y'.

Question

Y'(-6,2)
Y'(-2,-6)
Y'(2,-6)
Y'(6,-2)

Answer 1

To find the image of point Y(-2,6) after a 180-degree counterclockwise rotation about the origin, we can use the rotation formulas.

When a point \((x, y)\) is rotated 180 degrees counterclockwise about the origin, its new coordinates become \((-x, -y)\).

So, for point Y(-2, 6): \[ Y' = (-(-2), -(6)) = (2, -6) \]

Thus, the coordinates of Y' after the 180-degree rotation are \(Y'(2, -6)\).

The correct answer is: Y'(2, -6)