April 25th, 2019, 01:06 PM  #1 
Senior Member Joined: Mar 2019 From: TTF area Posts: 106 Thanks: 1  Show these point form a square
Show ACDE is a square C=10,2 A=4,2 E=8,8 D=14,4 Last edited by skipjack; April 25th, 2019 at 08:38 PM. 
April 25th, 2019, 01:17 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717 
They don't. Side lengths are different.

April 25th, 2019, 03:49 PM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics 
Should be $A = (4,2)$. Also, what have you tried?

April 25th, 2019, 04:01 PM  #4 
Senior Member Joined: Mar 2019 From: TTF area Posts: 106 Thanks: 1  Yes you're correct. I know it's a square. I have found all side lengths to be approximately 7.21 units or √52 and the diagonal from AD and CE are √104 or approximately 10.19 units and they are all at right angles to each other. What are some mathematical statements I can use?
Last edited by skipjack; April 25th, 2019 at 08:35 PM. 
April 25th, 2019, 11:18 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,935 Thanks: 2209 
The easiest approach is to show that the diagonals are mutually perpendicular and have a common midpoint. This suffices to establish that ACDE is a square and doesn't require use of Pythagoras.

April 26th, 2019, 01:36 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717 
If all angles are right angles and side lengths the same, it is a square.

April 26th, 2019, 01:45 PM  #7 
Member Joined: Feb 2019 From: United Kingdom Posts: 44 Thanks: 3 
This makes me cry. Use vectors!


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