Answer:
(10, 6)
Explanation:
The x and y coordinates of a point (x, y) that partitioned a segment that goes from (x1, y1) to (x2, y2) by fraction of m/n are calculated as:
[tex]\begin{gathered} x-\text{coordinate = }\frac{m}{n}(x_2-x_1)+x_1 \\ y-\text{coordinate}=\frac{m}{n}(y_2-y_1)+y_1 \end{gathered}[/tex]So, replacing (x1, y1) by A(16, 8), (x2, y2) by B(1, 3), and the fraction m/n by 2/5, we get
[tex]\begin{gathered} x-\text{coordinate = }\frac{2}{5}(1-16)+16=\frac{2}{5}(-15)+16=-6+16=10 \\ y-\text{coordinate}=\frac{2}{5}(3-8)+8=\frac{2}{5}(-5)+8=6 \end{gathered}[/tex]Therefore, the coordinate of the point that divided the segments into 2/5 is (10, 6).
