What outcome does a 180-degree rotation have on a point located at (x, y)?

What outcome does a 180-degree rotation have on a point located at (x, y)?

• A. (x, y)
• B. (-x, y)
• C. (-x, -y)
• D. (x, -y)

Answer: (C)

A 180-degree rotation results in the point being reflected through the origin. For a point initially positioned at (x, y), when you perform a 180-degree rotation, you move the point to a position directly opposite its original location on the Cartesian plane. To visualize this, consider the cartesian axes. A rotation of 180 degrees flips the point across both the x-axis and the y-axis. Consequently, the x-coordinate changes from x to -x, and the y-coordinate changes from y to -y. This transformation yields the new coordinates (-x, -y). Therefore, after a 180-degree rotation, the coordinates of the point (x,y) transform to (-x, -y), confirming that this is the correct outcome.

A 180-degree rotation results in the point being reflected through the origin. For a point initially positioned at (x, y), when you perform a 180-degree rotation, you move the point to a position directly opposite its original location on the Cartesian plane.

To visualize this, consider the cartesian axes. A rotation of 180 degrees flips the point across both the x-axis and the y-axis. Consequently, the x-coordinate changes from x to -x, and the y-coordinate changes from y to -y. This transformation yields the new coordinates (-x, -y).

Therefore, after a 180-degree rotation, the coordinates of the point (x,y) transform to (-x, -y), confirming that this is the correct outcome.