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Three vertices of  ▱ ABCD are B(-3, 3), C(2, 7), and D(5, 1). Find the coords of vertex A.

 

Please show work as well, thx!

 Jan 28, 2016

Best Answer 

 #1
avatar+128053 
+10

I learned this trick from heureka.......we have 3 possibilities.....each one is found by adding two of the points and subtracting the remaining one.....so

 

Point 1  = (-3, 3), (2, 7),  - (5, 1)   =   [ -3 + 2 -5, 3 + 7 -1]  = [ -6, 9]  = A

 

Here's the graph of this one: https://www.desmos.com/calculator/gn28jpviah

 

However....the points are out of order, here!!

 

Point 2  = (-3,3) + (5,1) - (2,7)  =   [ -3 +5  -2, 3 + 1 -7] = [-3, -3]  = A

 

Here's the graph of this one : https://www.desmos.com/calculator/au5lye4htm

 

Point 3  = (2,7) + (5,1) - (-3, 3)  = [ 2 + 5 + 3, 7 + 1 -3]  =  [ 10, 5]   = A

 

This one is OK

 

Here's the graph of this one : https://www.desmos.com/calculator/fi07fvmpps

 

The points are ot of order here, too

 

Note that each different point forms a different paralelogram, but only the second one produces the points in the correct order.....!!!!

 

 

cool cool cool

 Jan 28, 2016
edited by CPhill  Jan 28, 2016
 #1
avatar+128053 
+10
Best Answer

I learned this trick from heureka.......we have 3 possibilities.....each one is found by adding two of the points and subtracting the remaining one.....so

 

Point 1  = (-3, 3), (2, 7),  - (5, 1)   =   [ -3 + 2 -5, 3 + 7 -1]  = [ -6, 9]  = A

 

Here's the graph of this one: https://www.desmos.com/calculator/gn28jpviah

 

However....the points are out of order, here!!

 

Point 2  = (-3,3) + (5,1) - (2,7)  =   [ -3 +5  -2, 3 + 1 -7] = [-3, -3]  = A

 

Here's the graph of this one : https://www.desmos.com/calculator/au5lye4htm

 

Point 3  = (2,7) + (5,1) - (-3, 3)  = [ 2 + 5 + 3, 7 + 1 -3]  =  [ 10, 5]   = A

 

This one is OK

 

Here's the graph of this one : https://www.desmos.com/calculator/fi07fvmpps

 

The points are ot of order here, too

 

Note that each different point forms a different paralelogram, but only the second one produces the points in the correct order.....!!!!

 

 

cool cool cool

CPhill Jan 28, 2016
edited by CPhill  Jan 28, 2016

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