The coordinates of the point that partitions PT is (5, 11).
Solution:
Given P(2, 2) and T(7, 17).
Line segment PT is divided the coordinates of the point in the ratio 3 : 2.
Let R be the divided point the line segment PT.
Section Formula:
The point (x, y) which divides the line segment of the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the ratio m : n is
[tex]$\left(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}\right)[/tex]
Here [tex]x_1=2,y_1=2,x_2=7,y_2=17[/tex] and m = 3, n = 2
Substitute these in the given formula.
[tex]$R(x)=\left(\frac{3\times 7 + 2\times2}{3+2}, \frac{3\times17 + 2\times2}{3+2}\right)[/tex]
[tex]$R(x)=\left(\frac{21 + 4}{5}, \frac{51 + 4}{5}\right)[/tex]
[tex]$R(x)=\left(\frac{25}{5}, \frac{55}{5}\right)[/tex]
[tex]$R(x)=(5, 11)[/tex]
Hence the coordinates of the point that partitions PT is (5, 11).
