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  • If coordinates of two adjacent vertices of a parallelogram are (3, 2), (1, 0) and diagonals bisect each other at (2, –5), find coordinates of the other two vertices.     <div s

If coordinates of two adjacent vertices of a parallelogram are (3, 2), (1, 0) and diagonals bisect each other at (2, –5), find coordinates of the other two vertices.

 

 
 
 
 
 

Answers (1)

we know that , diagonals of parallelogram bisects each other , hence point O is midpoint of line AC and BD 

 

A ( 3,2) \: \: \:, \: O(2,-5)\: \: \: ,\: \: B(1,0)\\\\.\: \: \: \: \: \: \downarrow \: \:\: \: \: \: \: \: \: \: \: \: \: \: \downarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \downarrow\\\\ (x_1,y_1)\: \:\: \: \: \: \: (x,y) \: \:\: \: \: \: \: \: \: \: \: ( x_2,y_2)\\\\ C( x_3,y_3)\: \: \:\: \: \: \: D(x_4,y_4)

Since O is the midpoint of AC 

X = \frac{x_1 + x _3 }{2}\;\;\;\;, y = \frac{y _ 1 + y _ 3 }{2} \\\\ 2 = \frac{3+ x _3}{2} \: \: \: \:, - 5 = \frac{2+ y _3 }{2} \\\\ x_3 = 1 , y _ 3 = -12

Coordinates of point C are (1,-12) 

similarly point O is the midpoint of BD 

X = \frac{x_2 + x _4 }{2}\;\;\;\;, y = \frac{y _ 1 + y _ 4}{2} \\\\ 2 = \frac{1+ x _4}{2} \: \: \: \:, - 5 = \frac{0+ y _4 }{2} \\\\ x_4 = 3 , y _ 4 = -10

Coordinates of point D are (3,-10) 

Posted by

Safeer PP

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