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MathNet 2021 — Part 01 Question 18

Math Olympiad Vault · MathNet 2021 — Part 01

Question 18

Distinct lines $\ell$ and $m$ lie in the $xy$-plane. They intersect at the origin. Point $P(-1, 4)$ is reflected about line $\ell$ to point $P'$, and then $P'$ is reflected about line $m$ to point $P''$. The equation of line $\ell$ is $5x - y = 0$, and the coordinates of $P''$ are (4, 1). What is the equation of line $m$?
  1. $5x + 2y = 0$
  2. $3x + 2y = 0$
  3. $x - 3y = 0$
  4. $2x - 3y = 0$
  5. $5x - 3y = 0$