Respuesta :
Assume X(3,2) and Y(6,8).
Let Z be the point which is 3/5 of the way between XY. So,
[tex]\begin{gathered} XZ=\frac{3}{5}XY \\ \frac{XZ}{XY}=\frac{3}{5} \\ \frac{XY}{XZ}=\frac{5}{3} \\ \frac{XZ+ZY}{XZ}=\frac{5}{3} \\ \frac{ZY}{XZ}=\frac{5}{3}-1 \\ =\frac{2}{3} \end{gathered}[/tex]So point Z divide the line XY in ratio 3:2.
The coordinate of point P if it divide the line A(x_1,y_1) and B(x_2,y_2) in ratio m:n is,
[tex](x,y)=(\frac{nx_1+mx_2}{m+n},\frac{ny_1+my_2}{m+n})[/tex]Determine the coordinate of point the divide the line joining points (3,2) and (6,8) in 3:2 ratio.
[tex]\begin{gathered} (x,y)=(\frac{2\cdot3+3\cdot6}{3+2},\frac{2\cdot2+3\cdot8}{3+2}) \\ =(\frac{6+18}{5},\frac{4+24}{5}) \\ =(\frac{24}{5},\frac{28}{5}) \end{gathered}[/tex]So value of coodinate is (24/5,28/5)
