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)

A. (6,7)
B. (7,6)
C. (3,5)
D. (5,4)

Answer 1

B. (7,6)

Explanation:

When a line segment is divided in the ratio m:n, the coordinate of the point of internal division P is derived using the formula:

`P(x,y)=((mx_2+nx_1)/(m+n) ,(my_2+ny_1)/(m+n) )`

In this case, m:n=5:1

`(x_1,y_1)=(2,1), (x_2,y_2)=(8,7)\\P(x,y)=((5*8+1*2)/(5+1) ,(5*7+1*1)/(5+1) )\\=((42)/(6) ,(36)/(6) )\\P(x,y)=(7,6)`

The correct option is B.