ABC is an equilateral triangle and AD is the altitude on BC. If the coordinates of A are (1,2) and that of D are (-2,6) then what is the equation of BC?

Explanation

The slope of altitude AD is \frac{6-2}{-2-1} = -\frac{4}{3}. Since AD is perpendicular to BC, the slope of BC is \frac{3}{4}. BC passes through D(-2,6). Its equation is y-6 = \frac{3}{4}(x+2) \implies 4y-24 = 3x+6 \implies 3x-4y+30=0.

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