△ABC中,A(2,-1),B(-3,2),C(0,-4).三边BC,AB,AC中点依次是D,E,F.且EF交AD于M.求向量DM的坐标.

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△ABC中,A(2,-1),B(-3,2),C(0,-4).三边BC,AB,AC中点依次是D,E,F.且EF交AD于M.求向量DM的坐标.
△ABC中,A(2,-1),B(-3,2),C(0,-4).三边BC,AB,AC中点依次是D,E,F.且EF交AD于M.求向量DM的坐标.

△ABC中,A(2,-1),B(-3,2),C(0,-4).三边BC,AB,AC中点依次是D,E,F.且EF交AD于M.求向量DM的坐标.
D = (B+C)/2 = (-1.5,-1);
E = (A+B)/2 = (-0.5,0.5);
F = (A+C)/2 = (1,-2.5);
EF = E + (F-E)*t = (1.5*t-0.5,0.5-3*t);
AD = A + (D-A)*t = (-3.5*t+2,-1);
t = 0.5;
M=(0.25,-1)
DM = M-D

D(-3/2,-1),DA(7/2,0)dm(7/4,0)