if (1,2) (4,y) (x,6) and (3,5) are the vertices of a parallelogram taken in order. find xand y
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LetA = (1,2), B = (4, y), C= (x, 6) and D= (3, 5)
We know that diagonals of parallelogram bisect each other. It means that coordinates of midpoint of diagonalACwould be same as coordinates of midpoint of diagonalBD------(1)
UsingSection formula, the coordinates of midpoint ofACare:
(1+x2,(2+6)2)=((1+x)2,4)
Using Section formula, the coordinates of midpoint ofBDare:
((4+3)2,(5+y)2)=(72,(5+y)2)
According to condition(1),we have(1+x)2=72
⇒(1+x)=7
⇒x=6
According to condition(1),we also have4=5+y2
⇒8=5+y
⇒y=3
Therefore,x=6andy=3
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