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1980 AMC 12 Question 12

AMC12 · 1980 AMC 12

Question 12

The equations of $L_1$ and $L_2$ are $y=mx$ and $y=nx,$ respectively. Suppose $L_1$ makes twice as large an angle with the horizontal (measured counterclockwise from the positive $x$-axis) as does $L_2,$ and that $L_1$ has $4$ times the slope of $L_2.$ If $L_1$ is not horizontal, then $mn$ is
  1. $\frac{\sqrt2}{2}$
  2. $-\frac{\sqrt2}{2}$
  3. $2$
  4. $-2$
  5. not uniquely determined by the given information