Rotation axes and shifting origin Leave a Comment / Math / By Science++ Change of Axis : Rotation in axes and shifting in origin.1.Shifting of origin without Rotation of Axes :Initial : Origin = O( 0 , 0) X-axis = OX Y-axis = OY Point = P( x, y ) After Shifting : Origin = O’ (a , b ) X-axis = O’X’ Y-axis = O’Y’ Point = P( x’, y’ )Here you can see OX and OY are parallel to O’X’ and O’Y’Then , x = x’ + a , y = y’ + b2. Rotation of Axes without Shifting the origin :Initial : Origin = O( 0 , 0) X-axis = OX Y-axis = OY Point = P( x, y ) After rotation : Origin = O (0 , 0 ). Not changed X-axis = OX’ Y-axis = OY’ Rotation angle = θ ( anti-clockwise ) ∠X’OX = ∠YOY’ = θ Point = P( x’, y’ )Then , x = x’ cos θ – y’sin θ , y = x’ sin θ + y’cos θ 3.Shifting of origin and Rotation of Axes :Initial : Origin = O( 0 , 0) X-axis = OX Y-axis = OY Point = P( x, y ) After rotation and shifting : Origin = O’ (a , b ). X-axis = O’X’ Y-axis = O’Y’ Rotation angle = θ ( anti-clockwise )∠X’OX = ∠YOY’ = θ Point = P( x’, y’ )Then , x = a + x’ cos θ – y’sin θ , y = b + x’ sin θ + y’cos θ , [dflip id=”2281″][/dflip]