Respuesta :
We have been given two points. [tex]A(3,4)[/tex] and [tex]C(3,9)[/tex]. We are asked to find the point B such that it divides line segment AC so that the ratio of AB to BC is 4:1.
We will use segment formula to solve our given problem.
When a point P divides segment any segment internally in the ratio [tex]m:n[/tex], then coordinates of point P are:
[tex][\right x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}\left][/tex]
[tex](x_1,y_1)=(3,4)[/tex] and [tex](x_2,y_2)=(3,9)[/tex].
[tex]m=4,n=1[/tex]
Upon substituting our given information in above formula, we will get:
[tex][\right x=\frac{4(3)+1(3)}{4+1},y=\frac{4(9)+1(4)}{4+1}\left][/tex]
[tex][\right x=\frac{12+3}{5},y=\frac{36+4}{5}\left][/tex]
[tex][\right x=\frac{15}{5},y=\frac{40}{5}\left][/tex]
[tex][\right x=3,y=8\left][/tex]
Therefore, the coordinates of point B would be [tex](3,8)[/tex].
