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 

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

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