Respuesta :
Let (x,y) and (v,w) two points, if (p,q) divides the segment with end points (x,y) and (v,w) at a ratio a:b we can set the following equalities:
[tex]\begin{gathered} p=\frac{x+v\cdot\frac{a}{b}}{1+\frac{a}{b}}. \\ q=\frac{y+w\cdot\frac{a}{b}}{1+\frac{a}{b}} \end{gathered}[/tex]Substituting the given data we get that:
[tex]\begin{gathered} p=\frac{2+17\cdot\frac{2}{3}}{1+\frac{2}{3}}, \\ q=\frac{4+14\cdot\frac{2}{3}}{1+\frac{2}{3}} \end{gathered}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} p=\frac{2+\frac{34}{3}}{\frac{5}{3}}=\frac{\frac{40}{3}}{\frac{5}{3}}=8, \\ q=\frac{4+\frac{28}{3}}{\frac{5}{3}}=\frac{\frac{40}{3}}{\frac{5}{3}}=8. \end{gathered}[/tex]Therefore the coordinates of point P such that the segment with endpoints A (2, 4) and B (17, 14) in a ratio of 2:3 are (8,8).
Answer:
[tex]P(8,8)\text{.}[/tex]
