Question

If the point P changs to (4,-3) WHEN the angle are rotated through an angle 135^degree find the co coordinate of p with respect to origional system

Answer 1

When axes are rotated through an angle theta (@)

NOTE : we have taken theta as symbol '@'

then, x = xcos@ - ysin@

y = ycos@ - xsin@

when (x,y) are intial coordinates and (x, y ) are new coordinates,

$x = 4( \frac{ - 1}{ \sqrt{2} } ) (- 3) \: ( \frac{ - 1}{ \sqrt{2} } ) = \frac{ - 1}{ \sqrt{2} } \\ y = 4( \frac{1}{ \sqrt{2} } ) - 3( \frac{ - 1}{ \sqrt{2} } ) = \frac{7}{ \sqrt{2} }$

: (x,y) = ( -1/√2 , 7/√2 )..

Thank you :)