Answer:
D = (-4, -4)
Step-by-step explanation:
Given;
midpoint of line CD = M(-3, -7)
coordinate of C = (-2, -10)
The coordinate of D is calculated as follows;
C(-2, -10)---------------------M(-3, -7)--------------------D
[tex]M = \frac{D_1 + C_1}{2} \ , \ \frac{D_2 + C_2}{2} \\\\(-3, \ -7) = \frac{D_1 + (-2)}{2} , \ \frac{D_2 + (-10)}{2} \\\\(-3, \ -7) = \frac{D_1 \ - \ 2}{2} , \ \frac{D_2 -10}{2} \\\\-3 = \frac{D_1 \ - \ 2}{2} \ \ ----(1)\\\\-7 = \frac{D_2 -10}{2} \ -----(2)\\\\From \ (1): 2(-3) = D_1\ - \ 2\\\\-6 = D_1 - 2\\\\-6 + 2 = D_1\\\\-4 = D_1\\\\From \ (2) : \ 2(-7) = D_2 - 10\\\\-14 = D_2 - 10\\\\ -14 + 10 = D_2\\\\-4 = D_2\\\\The \ coordinate \ of \ D = (D_1\ , \ D_2)\\\\D = (-4 \ , \ -4)[/tex]
Therefore, the coordinate of D = (-4, -4)
