In the rectangular coordinate system, there are four points a (- 8, 3), B (- 4, 5), C (0, n), D (m, 0). When the perimeter of the quadrilateral ABCD is the shortest, we can find the value of Mn

In the rectangular coordinate system, there are four points a (- 8, 3), B (- 4, 5), C (0, n), D (m, 0). When the perimeter of the quadrilateral ABCD is the shortest, we can find the value of Mn

Let a (- 8,3) be a symmetric point a '(- 8, - 3) about X axis and B' (- 4,5) be a symmetric point B '(4,5) about y axis. Let the equation of a' B 'be y = KX + B (K ≠ 0), then − 3 = - 8K + B5 = 4K + B, and the solution is k = 23, B = 73. Therefore, the analytical formula of the line passing a' B 'is y = 23x + 73, the intersection of a' B 'and X axis D (m, 0), and the intersection with Y axis C (0, n), and M = - 72 can be obtained , n = 73, so Mn = - 32