If (1,2) (4,y) (x,6) and (3,5) are the vectecs of llgm orden the find the value of x,y

If (1,2) (4,y) (x,6) and (3,5) are the vectecs of llgm orden the find

1.	If (1,2) (4,y) (x,6) and (3,5) are the vectecs of llgm orden the find the value of x,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