To rotate a point counterclockwise by 90 degrees around the origin, you can use the following transformation for a point \((x, y)\):
\[ (x', y') = (-y, x) \]
Given point \(A(2, 4)\):
- The x-coordinate is \(2\) and the y-coordinate is \(4\).
- Applying the transformation:
- The new x-coordinate \(x' = -y = -4\)
- The new y-coordinate \(y' = x = 2\)
Thus, the new point after rotating \(A(2, 4)\) by 90 degrees counterclockwise is:
\[ A'(-4, 2) \]
Point \(A'(-4, 2)\) is located in Quadrant II, as the x-coordinate is negative and the y-coordinate is positive.