Final answer:
The coordinates of point T' after a 180-degree rotation around the origin are (2, -5).
Step-by-step explanation:
The coordinates of point T', the image of point T(-2,5) after a rotation of 180 degrees about the origin, are found using the rotation transformation equations for a point (x, y):
- x' = x cos(180°) - y sin(180°)
- y' = x sin(180°) + y cos(180°)
Since cos(180°) = -1 and sin(180°) = 0, the transformed coordinates (x', y') are
- x' = (-2) * (-1) - 5 * 0 = 2
- y' = (-2) * 0 + 5 * (-1) = -5
Therefore, the coordinates of T' are (2, -5).