To determine the new position of point A (2, 4) after a 270-degree counterclockwise rotation, we can use the rotation transformation formula for rotation about the origin (0,0).
The rotation transformation for a counterclockwise rotation by an angle θ is given by the following equations:
- \( x' = x \cdot \cos(\theta) - y \cdot \sin(\theta) \)
- \( y' = x \cdot \sin(\theta) + y \cdot \cos(\theta) \)
For a 270-degree rotation, we use \(\theta = 270^\circ\):
- \(\cos(270^\circ) = 0\)
- \(\sin(270^\circ) = -1\)
Plugging in the coordinates of point A (2, 4):
- \( x' = 2 \cdot 0 - 4 \cdot (-1) = 0 + 4 = 4 \)
- \( y' = 2 \cdot (-1) + 4 \cdot 0 = -2 + 0 = -2 \)
Thus, after a 270-degree counterclockwise rotation, the new coordinates are (4, -2).
Therefore, the answer is:
(4, −2)