Equilateral triangle

Elize · February 23rd, 2018, 06:21 AM

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.

skipjack · February 23rd, 2018, 09:33 AM

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.

February 23rd, 2018, 06:21 AM	#1
Elize Newbie Joined: Feb 2018 From: Iran Posts: 29 Thanks: 3	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 09:13 AM.
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February 23rd, 2018, 09:33 AM	#2
skipjack Global Moderator Joined: Dec 2006 Posts: 20,269 Thanks: 1958	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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