If the axes are rotated through an angle 45 ° , the coordinates of the point ( 2 2 , - 3 2 ) in the new system are

Step-by-step solution

If the coordinate axes are rotated through an angle θ , then a point P ( x ,   y ) will have co-ordinate P ( x ' ,   y ' ) Where x ' = x cos θ + y sin θ and y ' = y cos θ - x sin θ Here, x ,   y = 2 2 ,   - 3 2 and θ = 45 ° Now, x ' = 2 2 cos 45 ° - 3 2 sin 45 ° ⇒ x ' = 2 2 × 1 2 - 3 2 × 1 2 ⇒ x ' = 2 - 3 = - 1 And, y ' = - 3 2 cos 45 ° - 2 2 sin 45 ° y ' = - 3 2 × 1 2 - 2 2 &#21