Reflecting the point (2,-1) about y-axis, coordinate axes are rotated at an angle of 45 degrees in negative direction without - Maths - Straight Lines

Question

Reflecting the point (2,-1) about y-axis, coordinate axes are
rotated at an angle of 45 degrees in negative direction without
shifting the origin the new coordinates of the points are __?

Manbar Singh · Accepted Answer

The given point is 2,-1
Now, the reflection of point P about y-axis is P-2,-1
Let x,y and X,Y be the coordinates of the point P referred to old and new axes respectively
When the axes are rotated through θ = 45°, then    X = x cos θ + y sin θ⇒X = -2 cos 45° + -1 sin 45°⇒X = -22 - 12 = -32    Y = - x sin θ + y cos θ⇒Y = 2 sin 45° - 1 × cos 45°⇒Y = 22-12 = 12So, new coordinates of P are -32,12

Reflecting the point (2,-1) about y-axis, coordinate axes are rotated at an angle of 45 degrees in negative direction without shifting the origin. the new coordinates of the points are __?