What is the new position of point (0, 2) after a 180-degree rotation?

What is the new position of point (0, 2) after a 180-degree rotation?

• A. (0, 2)
• B. (-2, 0)
• C. (0, -2)
• D. (2, 0)

Answer: (C)

To determine the new position of the point (0, 2) after a 180-degree rotation about the origin, we can analyze how points are transformed with this rotation. When a point is rotated 180 degrees around the origin, both its x-coordinate and y-coordinate change their signs. Specifically, if the original point is represented as (x, y), after a 180-degree rotation, its new coordinates will be (-x, -y). Applying this to the point (0, 2): - The x-coordinate is 0, which remains 0 after the sign change (since -0 = 0). - The y-coordinate is 2. Changing the sign gives us -2 (since -2 is the opposite of 2). Thus, the new position of the point (0, 2) after a 180-degree rotation is (0, -2). This makes the answer (0, -2) the correct response in this scenario.

To determine the new position of the point (0, 2) after a 180-degree rotation about the origin, we can analyze how points are transformed with this rotation.

When a point is rotated 180 degrees around the origin, both its x-coordinate and y-coordinate change their signs. Specifically, if the original point is represented as (x, y), after a 180-degree rotation, its new coordinates will be (-x, -y).

Applying this to the point (0, 2):

• The x-coordinate is 0, which remains 0 after the sign change (since -0 = 0).

• The y-coordinate is 2. Changing the sign gives us -2 (since -2 is the opposite of 2).

Thus, the new position of the point (0, 2) after a 180-degree rotation is (0, -2). This makes the answer (0, -2) the correct response in this scenario.