The point S(2, -6) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, S′?
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The point W(
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2,6) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, W'?
The point S(2, -6) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, S′?
To find the coordinates of the resulting point S' after rotating point S(2, -6) 180° counterclockwise around the origin, we can use the following steps:
1. Understand the rotation: Rotating a point 180° counterclockwise around the origin simply means flipping the point over the x-axis and y-axis simultaneously.
2. Apply the rotation: Flipping a point over the x-axis means changing the sign of its y-coordinate, and flipping a point over the y-axis means changing the sign of its x-coordinate.
3. Calculate the new coordinates: Applying the rotations, the x-coordinate of S' will be the negative of the original y-coordinate, and the y-coordinate of S' will be the negative of the original x-coordinate.
- The x-coordinate of S' = -(-6) = 6
- The y-coordinate of S' = -(2) = -2
Therefore, the coordinates of the resulting point S' after rotating S(2, -6) 180° counterclockwise around the origin are S'(6, -2).