When the axes are rotated through an angle 45 ° , the new coordinates of a point P are ( 1 , - 1 ) . The coordinates of P in the original system are

Step-by-step solution

When axes are rotated through an angle θ , then coordinates are X = x cos θ - y sin θ = cos 45 ∘ + sin 45 ∘   = 1 2 + 1 2 = 2 Y = x sin θ + y cos θ   = sin 45 ∘ - cos 45 ∘ = 1 2 - 1 2 = 0 Therefore, the coordinates of P in the original system are ( 2 , 0 )