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Lines are Fun!

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December 31, 2005
analytic geometrygraphing linesslopetrigonometry

Problem Statement

The equations of L1L_1 and L2L_2 are y=mxy=mx and y=nxy=nx, respectively. Suppose L1L_1 makes twice as large of an angle with the horizontal (measured counterclockwise from the positive x-axis ) as does L2L_2, and that L1L_1 has 4 times the slope of L2L_2. If L1L_1 is not horizontal, then mnmn is (A) 22(B) −22(C) 2(D) −2(E) not uniquely determined\text{(A)} \ \frac{\sqrt{2}}{2} \qquad \text{(B)} \ -\frac{\sqrt{2}}{2} \qquad \text{(C)} \ 2 \qquad \text{(D)} \ -2 \qquad \text{(E)} \ \text{not uniquely determined}
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