Question

Find the coordinates of point P, so that P partitions the directed

segment TD in the ratio 5:1, if T (2,1) and D (8,7).

Answer 1

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:

`[\Left x=(mx_2+nx_1)/(m+n),y=(my_2+ny_1)/(m+n)] \right`

`m=5, n=1`,
`(x_1,y_1)=(2,1)` and
`(x_2,y_2)=(8,7)`.

Upon substituting our given information in above formula, we will get:

`[\Left x=(5(8)+1(2))/(5+1),y=(5(7)+1(1))/(5+1)] \right`

`[\Left x=(40+2)/(6),y=(35+1)/(6)] \right`

`[\Left x=(42)/(6),y=(36)/(6)] \right`

`[\Left x=7,y=6] \right`

Therefore, the coordinates of point P are (7,6).