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The points with coordinates (1,1), (3,5), and (-1,4) are three vertices of a parallelogram.  Find all possible coordinates of the fourth vertex.

 Dec 17, 2019
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(1,1), (3,5), and (-1,4)

 

There will  be three possibilities

 

We can find each by adding  the coordinates of any two of the points  and subtracting the  coordinates of the remaining point

 

So  we  have

 

(1, 1) + ( 3,5)  - ( -1, 4)  =   ( 5, 2)

(1, 1) + ( -1, 4)  - (3,5)  =  (-3, 0)

(3,5) + ( -1, 4) - (1,1)  =  ( 1, 8)

 

Here's a pic :   https://www.desmos.com/calculator/jvrousklbs

 

 

cool cool cool

 Dec 17, 2019

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