Answer:
[tex]B = (3, 3)[/tex]
Step-by-step explanation:
From the given graph the coordinates of A are (8,1) and coordinates of C are (-7,7).
The point B lies on the given line AC and divides the line such that [tex]AB = \frac{1}{3}AC[/tex]
Thus, it can be said that the point B divides the line in the ratio 1:2.
By, section formula we have:
[tex]B = \bigg(\displaystyle\frac{mx_2 + nx_1}{m+n}, \displaystyle\frac{my_2 + ny_1}{m+n}\bigg)[/tex]
where, m:n is the ration in which the line is divided.
Here,
[tex]m:n = 1:2\\(x_1, y_1) = (8,1)\\(x_2, y_2) = (-7,7)[/tex]
Putting, all the values, we have,
[tex]B = \bigg(\displaystyle\frac{-7 + 16}{3}, \displaystyle\frac{7 + 2}{3}\bigg)[/tex]
[tex]B = (3, 3)[/tex]
