November 21st, 2016, 12:36 PM  #1 
Newbie Joined: Nov 2016 From: Egypt Posts: 1 Thanks: 0  Coordinate problem
Hello and welcome, this is my first post in this forum, probably going to be the last.. because I came here because of this problem anyways.. but I hope not.. it's in Arabic,as I'm an Egyptian.. so forgive me if I'm mistaken in something " Prove that the points A(5,1) , B(1,3) , C(5,3) are Heads of a Rightangled Triangle in B.. Then find the coordinate of Point D that makes ABCD a Rectangle.. " Saving you time: AB's length is going to be √32, BC = √72 and AC = √104 and say we proved it's a rightangled Triangle in the angle B The common way of getting the Coordinate of D.. is by getting the midpoints of AC and DB.. and yyyyeah.. it goes on a bit but I want to get it another way, I told my teacher.. he tried to solve it that way but failed miserably lol.. there was something wrong. I wanted to Draw AD and DC, Then.. because it's a rectangle, I try to equate AD and BC,and Equate AB and DC.. How do I do it that way? (I'm going to include a " Picture ") I hope I explained correctly and enough for a valid solution,Thank you so much for reading this through though, even if you don't solve it Picture: Last edited by skipjack; August 7th, 2017 at 09:32 PM. 
August 7th, 2017, 09:39 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,707 Thanks: 1532 
D is (1,7). (Adding coordinates, A + C = B + D.)

August 9th, 2017, 05:58 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,969 Thanks: 807 
Or Since B is the right angle, add the vectors BA= <5 1, 1 (3)>= <4, 4> and BC= <5 1, 3(3)>= <6, 6> to get BD= <2, 10>= <x 1, y (3)>. 2= x 1 so x= 1 and 10= y+ 3 so y= 7. D is (1, 7).


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