Answer:
The coordinate of the point is; (0,2)
Step-by-step explanation:
The given line segment has points with coordinates A(−2,6)
and B(4,−6).
We want to find a point (x,y) that divides this line segment in the ratio:
m:n=2:4
The x-coordinate of this point is given by;
[tex]x=\frac{mx_2+nx_1}{m+n}[/tex]
We substitute [tex]x_1=-2,x_2=4,m=2,n=4[/tex]
[tex]\implies x=\frac{2*4+4*-2}{2+4}[/tex]
[tex]\implies x=\frac{8-8}{6}=0[/tex]
The y-coordinate of this point is given by;
[tex]y=\frac{my_2+ny_1}{m+n}[/tex]
We substitute [tex]y_1=6,y_2=-6,m=2,n=4[/tex]
[tex]\implies y=\frac{2*-6+4*6}{2+4}[/tex]
[tex]\implies y=\frac{-12+24}{6}=2[/tex]
The coordinate of the point is; (0,2)
