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An equilateral triangle has one vertex at (2, 3). If the side opposite to this vertex lies on the line x + y = 2, then the equations of the other two sides are

1. y - 3 = (2 ± √3)(x - 2)
2. y + 3 = (2 ± √3)(x + 2)
3. y + 3 = (3 ± √2)(x + 2)
4. y - 3 = (3 ± √2)(x - 2)

Correct answer: y - 3 = (2 ± √3)(x - 2)

Solution

The base x+y=2 has slope -1. Lines through the vertex (2,3) making 60 deg with it satisfy sqrt(3) = |(m+1)/(1-m)|, giving m = 2 +/- sqrt(3). Thus y - 3 = (2 +/- sqrt(3))(x - 2).

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