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′.
To rotate a point (x, y) about the origin by 180° counterclockwise, we can use the following formulas:
x' = -x
y' = -y
Using these formulas, we can find the coordinates of Y' as follows:
For point Y(-2, 6):
x' = -(-2) = 2
y' = -(6) = -6
Therefore, the coordinates of Y' are (2, -6).
To find the image of point Y after a 180° counterclockwise rotation about the origin, we need to swap the coordinates of Y and negate them.
The coordinates of Y are (-2, 6).
Swapping and negating the coordinates, we get Y' as (6, -2).
Therefore, the coordinates of Y' after the rotation are (6, -2).