(1,2) (4,y)(x,6)(3,5) are vertices of parallelogram find x and y.

1.	(1,2) (4,y)(x,6)(3,5) are vertices of parallelogram find x and y.
Answer» Let A → (1, 2), B → (4, y), C→ (x, 6) and D→ (3, 5).We know that the diagonals of parallelogram bisect each other.So, Coordinates of the mid-point of diagonal AC= Coordinates of the mid-point of diagonal BD{tex}\\Rightarrow \\left( {\\frac{{1 + x}}{2},\\frac{{2 + 6}}{2}} \\right) = \\left( {\\frac{{4 + 3}}{2},\\frac{{y + 5}}{2}} \\right){/tex}{tex}\\Rightarrow \\left( {\\frac{{1 + x}}{2},4} \\right) = \\left( {\\frac{7}{2},\\frac{{y + 5}}{2}} \\right){/tex}{tex}\\Rightarrow \\frac{{1 + x}}{2} = \\frac{7}{2}{/tex}{tex}\\Rightarrow{/tex} 1 + x = 7{tex}\\Rightarrow{/tex} x = 6and {tex}4 = \\frac{{y + 5}}{2}{/tex}{tex}\\Rightarrow{/tex} y + 5 = 8{tex}\\Rightarrow{/tex} y = 3

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