Respuesta :
Given :
First point (A) = (-2,4)
Second point (B) = (7,-2)
ratio is 1:2
If the point is :
[tex]\begin{gathered} (x_1,y_1)_{} \\ \text{and} \\ (x_2,y_{2)} \end{gathered}[/tex]line sigmrnt ratio is m:n then point is:
[tex](x^{\prime},y^{\prime})=(\frac{mx_1+nx_2}{m+n},\frac{my_1+ny_2}{m+n})[/tex]If
[tex]\begin{gathered} m=1 \\ n=2 \\ x_1=-2 \\ x_2=7 \\ y_1=4 \\ y_2=-2 \end{gathered}[/tex]a partition of AB in ratio 1:2
So "B" point distance from A point is:
[tex]\begin{gathered} =7-(-2) \\ =7+2 \\ =9 \end{gathered}[/tex]ratio is 1:2 would be divide is 1/3.
so distance 9 is:
[tex]\frac{9}{3}=3[/tex]Coordinates form A point is:
[tex]\begin{gathered} =3+(-2) \\ =3-2 \\ =1 \end{gathered}[/tex]Y coordinates B point to A point is:
[tex]\begin{gathered} =4-(-2) \\ =4+2 \\ =6 \end{gathered}[/tex]Ratio is 1:2 that mean:
[tex]\begin{gathered} =\frac{6}{3} \\ =2 \end{gathered}[/tex]y coordinates from A point is:
[tex]\begin{gathered} =4-2 \\ =2 \end{gathered}[/tex]So the point is (1,2)
