How to determine the coordinates of the point M?#A_(((2,-5)));B_(((-3,5)))#;And #vec(BM)=1/5vec(AB)#

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Answer 1 · 2018-05-02T18:50:01

# M=M(-4,7)#.

Suppose that, #M=M(x,y)#.

#:. vec(BM)=(x,y)-(-3,5)=(x+3,y-5)............(star_1)#.

# vec(AB)=(-3,5)-(2,-5)=(-5,10).................(star_2)#.

But, Given that, #vec(BM)=1/5vec(AB)#.

#:. (x+3,y-5)=1/5(-5,10)...[because, (star_1) & (star_2)]#.

#:. (x+3,y-5)=(-1,2)#.

#:. x+3=-1 and y-5=2#.

#:. x=-4 and y=7#.

#:. M(x,y)=M(-4,7)#.