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)

Question

asked Jun 9, 2021 119k views

1 Answer

Clemens Himmer · Answer 1 · 2021-06-12T22:19:17+0000

Answer:

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.