Question

If fyp is rotated under 180 degrees around the origin, what will be the coordinates of the image of point y?

A. The coordinates will remain the same.
B. The coordinates will be (x, -y).
C. The coordinates will be (-x, y).
D. The coordinates will be (-x, -y).

Answer 1

After a 180-degree rotation around the origin, the coordinates of point y would be (-x, -y), as both the x and y coordinates change their signs.

Step-by-step explanation:

When a point is rotated 180 degrees around the origin, the coordinates of the point are negated. Therefore, the coordinates of the image of point y after a 180-degree rotation would be (-x, -y). The rotation of a point (x, y) by 180 degrees around the origin results in the point essentially being reflected over both the x-axis and y-axis. This means that both the x-coordinate and the y-coordinate change their signs.

Using this rule, if we consider y as a point with coordinates (x, y), after a 180-degree rotation, the point would be located at coordinates (-x, -y). Therefore, the correct answer to the question is D. The coordinates will be (-x, -y).