Question

If the axes are rotated through an angle 180° in the positive direction, the new coordinates of (x,y) are
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Answer 1

Given :   coordinates  ( x , y)

axes are rotated through an angle 180 in the positive direction,

To find :  New coordinates

Solution:

'

When rotated at angle α then ( x , y)  becomes ( X , Y)

X   = xcosα + ysinα

Y =  -xsinα + ycosα

α  = 180°

=> X   = xcos 180° + ysin 180°  = - x

Y =  -xsinα + ycosα =  - y

Hence New coordinates of (x , y) are  ( - x , -y)

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