A graph of the triangle and its image after a 180 degrees rotation about the origin is shown on the cordinate plane in the picture below.
In Euclidean Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Furthermore, the mapping rule for the rotation of a geometric figure about the origin by 180° is given by this mathematical expression:
(x, y) → (-x, -y)
Point (1, 2) → New Point = (-1, -2)
Point (2, 4) → New Point = (-2, -4)
Point (4, 2) → New Point = (-4, -2)