Answer: Choice D) [tex]2\sqrt{5}[/tex]
===========================================================
Work Shown:
Point A starts at (-2,3) and moves to (2,5) after applying the translation rule of "shift 4 to the right, 2 up".
Use the distance formula to find the distance from (-2,3) to (2,5)
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-2)^2 + (3-5)^2}\\\\d = \sqrt{(-4)^2 + (-2)^2}\\\\d = \sqrt{16 + 4}\\\\d = \sqrt{20}\\\\d = \sqrt{4*5}\\\\d = \sqrt{4}*\sqrt{5}\\\\d = 2\sqrt{5}\\\\d \approx 4.472136\\\\[/tex]
