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, $vec(BM)=1/5vec(AB)$ .

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

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

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

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

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

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