AMC 10B 2021 Fall Problem 17

Distinct lines \ell and m lie in the x y-plane. They intersect at the origin. Point P(-1,4) is reflected about line \ell to point P^{\prime}, and then P^{\prime} is reflected about line m to point P^{\prime \prime}. The equation of line \ell is 5 x-y=0, and the coordinates of P^{\prime \prime} are (4,1). What is the equation of line m ?

Answer Choices
A. 5 x+2 y=0
B. 3 x+2 y=0
C. x-3 y=0
D. 2 x-3 y=0
E. 5 x-3 y=0