We are asked to find the coordinates of point P such that P partitions the directed segment TD in the ratio 5:1. The coordinates of both points are: T (2,1) and D (8,7).
We will use section formula to solve our given problem.
When a point Q divides a segment AB internally in the ratio m:n, then the coordinates of point Q are:
[tex][\Left x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}] \right[/tex]
[tex]m=5, n=1[/tex], [tex](x_1,y_1)=(2,1)[/tex] and [tex](x_2,y_2)=(8,7)[/tex].
Upon substituting our given information in above formula, we will get:
[tex][\Left x=\frac{5(8)+1(2)}{5+1},y=\frac{5(7)+1(1)}{5+1}] \right[/tex]
[tex][\Left x=\frac{40+2}{6},y=\frac{35+1}{6}] \right[/tex]
[tex][\Left x=\frac{42}{6},y=\frac{36}{6}] \right[/tex]
[tex][\Left x=7,y=6] \right[/tex]
Therefore, the coordinates of point P are (7,6).
