Question

已知M,N,P三点的坐标分别为(-1,0),(3,-1),(1,2),并且向量ME=1/3向量MP,向量NF=1/3向量

Answer 1

(1)

ME = 1/3 MP and NF = 1/3NP

Let O be the origin

OE = OM + ME

=(-1,0)+ ME

=(-1,0) + 1/3MP (ME=1/3MP)

=(-1,0) + 1/3(MO + OP)

=(-1,0) + 1/3(-OM + OP)

=(-1,0) + 1/3[ -(-1,0)+ (1,2) ]

=(-1/3,2/3)

i.e E(-1/3,2/3)

OF = ON + NF

= (3,-1) + 1/3(NP)

= (3,-1) + 1/3(-ON+OP)

= (3,-1) + 1/3[ -(3,-1)+(1,2) ]

= (3,-1) + (-2/3,1)

= (7/3,0)

i.e F(7/3,0)

(2)

EF = EO + OF

= -(-1/3,2/3) + (7/3,0)

= (8/3,-2/3)

MN = MO + ON

= -(-1,0) + (3,-1)

=(4,-1)

Ratio of x co-ordinate ,y co-ordinate of EF = (8/3)/(-2/3) = -4

Ratio of x co-ordinate ,y co-ordinate of MN = 4/-1 = -4

Therefore MN//EF