To determine the counter clockwise rotation of 180 degree about the origin
When rotating a point 180 degrees counterclockwise about the origin our point H(x,y) becomes H'(-x,-y).
[tex]\text{Initial coordinate of H = (-4 , 2)}[/tex]
From the rotation formula about the origin counterclockwise 180 degree is
[tex]\begin{gathered} \text{ Final coordinate of H}^{^{\prime}}\text{ = (-(-4) , -2)} \\ H^{\prime}\text{ = (4 , -2)} \end{gathered}[/tex]
Therefore the correct answer is Option A
