# Rotation axes and shifting origin

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’ + b

2. 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]

error: Content is protected !!