Rotate the point (0,4)(0, 4)(0,4) by 45∘45^\circ45∘ counter-clockwise about the origin.
(0,4)(0, 4)(0,4)
(4,0)(4, 0)(4,0)
(422,422)(\frac{4\sqrt{2}}{2}, \frac{4\sqrt{2}}{2})(242,242)
(−422,422)(-\frac{4\sqrt{2}}{2}, \frac{4\sqrt{2}}{2})(−242,242)