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November 21st, 2016, 12:36 PM   #1
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Post 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 Right-angled 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 right-angled 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

Last edited by skipjack; August 7th, 2017 at 09:32 PM.
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August 7th, 2017, 09:39 PM   #2
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D is (-1,7). (Adding coordinates, A + C = B + D.)
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August 9th, 2017, 05:58 AM   #3
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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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