If (3,3), (6,y), (x,7) and (5,6) are the vertices of a parallelogram taken in order, find the values of 'x' and 'y' .

Asked by  | 13th Mar, 2013, 12:28: AM

Expert Answer:

Answer : Given : (3,3), (6,y), (x,7) and (5,6) are the vertices of a parallelogram taken in order
To find : the values of 'x' and 'y'
 

Let A(3,3), B(6, y), C(x, 7) and D (5, 6) be the vertices of parallelogram ABCD.

We know that, diagonals of parallelogram bisect each other.

=>  Coordinate of mid point of diagonal BD = Coordinate of mid point of diagonal AC

Coordinates of mid point of diagonal BD = (5+6 )/2 , (6+y) /2 

                                                           = 11/2 , (6+y)/2 

Coordinate of mid point of diagonal AC = (3+x)/2 , (7+3)/2

                                                         = (3+x)/2 , 10/2                                                         

Now comparing the c xordinates of mid point of both diagnols 

=> 11/2 = (3+x)/2 

=> 11 = 3+ x

=> x = 8

similarily comparing y coordinates

=>  (6+y)/2 = 10/2 

=> 6+ y = 10

=> y = 4 

=> Answer : x =8  and y = 4 


Answered by  | 13th Mar, 2013, 12:49: AM

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