Equilateral triangle

Elize · February 23rd, 2018, 05:21 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, 08:33 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, 05:21 AM	#1
Elize Newbie Joined: Feb 2018 From: Iran Posts: 16 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 08:13 AM.
$Elize is offline$

February 23rd, 2018, 08:33 AM	#2
skipjack Global Moderator Joined: Dec 2006 Posts: 19,059 Thanks: 1619	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.
$skipjack is offline$

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Equilateral triangle	mared	Geometry	5	June 3rd, 2014 04:51 AM
An equilateral triangle...	Bigbigcool	Algebra	12	January 24th, 2012 06:52 AM
Equilateral Triangle...	julian21	Algebra	1	November 1st, 2010 06:53 PM
equilateral triangle	zgonda	Algebra	2	August 20th, 2010 08:13 AM
Equilateral triangle	Brooklyn	Algebra	1	October 10th, 2009 12:55 PM