Question

The midpoint of line CD is M(-3,-7). If the coordinates of C are (-2, -10), what are the coordinates of D?

Answer 1

D = (-4, -4)

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

`M = (D_1 + C_1)/(2) \ , \ (D_2 + C_2)/(2) \\\\(-3, \ -7) = (D_1 + (-2))/(2) , \ (D_2 + (-10))/(2) \\\\(-3, \ -7) = (D_1 \ - \ 2)/(2) , \ (D_2 -10)/(2) \\\\-3 = (D_1 \ - \ 2)/(2) \ \ ----(1)\\\\-7 = (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)`

Therefore, the coordinate of D = (-4, -4)