已知点A（－1，1），B（-4，5）及向量BC=向量3BA，AD=向量3AB，向量AE=向量1/2

Question

已知点A（－1，1），B（-4，5）及向量BC=向量3BA，AD=向量3AB，向量AE=向量1/2AB，求点C,D,E的坐标。急需答案步骤

Answer 1

BC=3BA, AD=3AB, AE=(1/2)AB

OC
= OB +BC
= OB + 3BA
= OB + 3(OA -OB)
=3OA-2OB
=(-3,3) -(-8,10)
=(5,-7)
C (5,-7)
OD = OA +AD
= OA + 3AB
= OA+3(OB-OA)
= 3OB - 2OA
= (-12,15)-(-2,2)
= (-10,13)
D(-10,13)
OE = OA+AE
=OA +1/2AB
= OA +1/2(OB-OA)
= 1/2(OB+OA)
=1/2((-4,5)+(-1,1))
= (-5/2, 3)
E(-5/2,3)