2021 Fall AMC 10B Problem 17

Two reflections across lines through the origin are equivalent to a rotation by twice the angle from the first reflecting line to the second. The point $(-1,4)$ is sent to $(4,1),$ which is a $90^\circ$ clockwise rotation. Therefore line $m$ is $45^\circ$ clockwise from line $\ell.$ The slope of $\ell$ is $5.$ If $\theta_m=\theta_\ell-45^\circ,$ then $$\tan\theta_m=\frac{5-1}{1+5}=\frac23.$$ Thus line $m$ is $y=\frac23x,$ or $2x-3y=0.$ Thus, the answer is D .