A graph of triangle T and its image after a rotation of 180° about the origin (0, 0) is shown on the coordinate grid 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')
Coordinates (2, 4) → Coordinates (-2, -4)
Coordinates (3, 1) → Coordinates (-3, -1)
Coordinates (1, 1) → Coordinates (-1, -1)