Mathematics

Problem

69. Rotating Coordinate Systems The `

x y

`-coordinate system is rotated through the angle `

45^{\circ}

` to obtain the `

x^{\prime} y^{\prime}

`-coordinate system. (a) If the coordinates of a point in the `

x y

`-coordinate system are `

(1,2)

`, what are the coordinates of the rotated point in the `

x^{\prime} y^{\prime}

`-coordinate system? (b) If the coordinates of a point in the `

x^{\prime} y^{\prime}

`-coordinate system are `

(1,2)

`, what are the coordinates of the point in the `

x y

`-coordinate system that was rotated to it?