Answer:
[tex](x, y) \rightarrow (-x, -y)[/tex]
Step-by-step explanation:
Rotation of any point in the form of (x, y) about the origin O through 180 degree in anticlockwise or counterclockwise direction, it will takes the new position (-x, -y)
i.e,
The rule of rotation about the origin through 180 degree is given by:
[tex](x, y) \rightarrow (-x, -y)[/tex]
For example:
Let the point A(-4, 6) rotate by the rule [tex]R_{0, 180^{\circ}}[/tex]
then;
[tex]A(-4, 6) \rightarrow (4, -6)[/tex]
⇒the coordinate of image of the point A is, (4, -6)
Therefore, the rule represents [tex]R_{0, 180^{\circ}}[/tex] is, [tex](x, y) \rightarrow (-x, -y)[/tex]
