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February 23rd, 2018, 05:21 AM   #1
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Unhappy Equilateral triangle

A vertex of an equilateral triangle is A(2,3) and the equation of opposite side is x+y+2=0. Find the equations of the other two sides. Please explain step by step.

Last edited by skipjack; February 23rd, 2018 at 08:13 AM.
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February 23rd, 2018, 08:33 AM   #2
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As the given side has slope tan(135°) = -1, the other sides have slopes tan(75°) = 2 + √3 and tan(15°) = 2 - √3, and so their equations are y = (2 ± √3)(x - 2) + 3.

The single equation x² - 4xy + y² + 8x + 2y - 11 = 0 suffices, as it can be factorized (or solved by using the quadratic formula) to give the above two equations.
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