Question

I don’t really get this one.
Thx and have a great day!!

Answer 1

The correct option is C). (9,4)

The coordinates of a point N is (9,4)

Explanation:

Theory: If point P(x,y) lies on line segment AB and AP: PB=m:n, then we say P divides line AB internally in ratio of m:n and Point is given by

P=
`((mX2+nX1)/(m+n) , (mY2+nY1)/(m+n))`

Given that point, M is lying somewhere between point L and point N.

The coordinates of a point L is (-6,14)

The coordinates of a point M is (-3,12)

Also, LM: MN = 1:4

We can write as,

Let,

Point L(-6,14)=(X1, Y1)

Point M(-3,12)=(x,y)

Point N is (X2, Y2)

m=1 and n=4

M(-3,12)=
`((mX2+nX1)/(m+n) , (mY2+nY1)/(m+n))`

M(-3,12)=
`((1(X2)+4(-6))/(1+4) , ((Y2)+4(14))/(1+4))`

M(-3,12)=
`(((X2)-24)/(5) , (1(Y2)+56)/(5))`

`(-3)=((X2)-24)/(5)`

(-15)=X2-24

X2=9

`(12)=((Y2)+56)/(5)`

(60)=Y2+56

Y2=4

Thus,

The coordinates of a point N is (9,4)

Result: The correct option is C). (9,4)