Answer:
[tex](4,7)[/tex]
Step-by-step explanation:
We are asked to find the coordinates of the the point that divides the line segment directed from Y to Z in the ratio of 2:1.
[tex]Y(6,3)=(x_1,y_1)[/tex] and [tex]Z(3,9)=(x_2,y_2)[/tex]
We will use section formula to solve our given problem.
When a point P divides a line segment AB internally in the ratio m:n, then
[tex][x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}][/tex]
[tex][x=\frac{2\cdot 3+1\cdot 6}{2+1},y=\frac{2\cdot 9+1\cdot 3}{2+1}][/tex]
[tex][x=\frac{6+6}{3},y=\frac{18+3}{3}][/tex]
[tex][x=\frac{12}{3},y=\frac{21}{3}][/tex]
[tex][x=4,y=7][/tex]
Therefore, the coordinates of point would be [tex](4,7)[/tex].
