The vertices A(x,2);B(3,4) and C(3,y),D(4,2) forms a parallelogram then x+y is
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Given : The vertices A(x, 2); B (3,4) and C (3, y), D (4,2) forms a parallelogram
To Find : x + y
Solution:
A(x, 2); B (3,4) and C (3, y), D (4,2)
Opposite sides of a parallelogram are parallel
Parallel lines have same slope
Slope of AB = Slope of CD
=> ( 2 - 4)/(x - 3) = (y - 2)/(3 - 4)
=> -2/(x - 3) = (y - 2)/-1
=> 2 = (x - 3)(y - 2)
Slope of AC = Slope of BD
(y - 2)/(3 - x) = (2 - 4)/(4 - 3)
=> (y - 2)/(3 - x) = -2
=> y - 2 = - 2(3 - x)
=> y - 2 = 2(x - 3)
2 = (x - 3)(y - 2)
=> 2 = = (x - 3) 2(x - 3)
=> (x - 3)² = 1
=> x - 3 = ± 1
=> x = 4 , 2
x = 4 not possible as then A & D will be same point
=> x = 2
=> y - 2 = 2(x - 3)
=> y - 2 = 2(2 - 3)
=> y = 0
x + y = 2 + 0 = 2
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