Answer:
The correct option is C). (9,4)
The coordinates of a point N is (9,4)
Step-by-step 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=[tex](\frac{mX2+nX1}{m+n} , \frac{mY2+nY1}{m+n})[/tex]
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)=[tex](\frac{mX2+nX1}{m+n} , \frac{mY2+nY1}{m+n})[/tex]
M(-3,12)=[tex](\frac{1(X2)+4(-6)}{1+4} , \frac{(Y2)+4(14)}{1+4})[/tex]
M(-3,12)=[tex](\frac{(X2)-24}{5} , \frac{1(Y2)+56}{5})[/tex]
[tex](-3)=\frac{(X2)-24}{5} [/tex]
(-15)=X2-24
X2=9
[tex](12)=\frac{(Y2)+56}{5} [/tex]
(60)=Y2+56
Y2=4
Thus,
The coordinates of a point N is (9,4)
Result: The correct option is C). (9,4)
