A SAR operates at a wavelength of 6 cm and is used for interferometric SAR observations. In position M, the radar has (x, y) coordinates (-400000, +800000) m, while in position S its coordinates are (-400100, +800000) m. A scatterer A located near the origin has coordinates (x, y).

(i) Show that the range from M to A is given approximately by 0.4472136x - 0.8944272y plus a constant, and that the difference between the range from S to A and the range from M to A is given approximately by 0.0000894x + 0.0000447y plus a constant.
(ii) Hence find the coordinates of A if its distance from M is the same as that from the origin, but the difference SA - MA is greater than SO - MO by half a wavelength.

(iii) If the system is capable of resolving 1/50 of a fringe, what is its effective height resolution? [Assume that z = 0 throughout this question.]