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

Answer:

B. (7,6)

Step-by-step 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:

$P(x,y)=(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n} )$

In this case, m:n=5:1

$(x_1,y_1)=(2,1), (x_2,y_2)=(8,7)\\P(x,y)=(\dfrac{5*8+1*2}{5+1} ,\dfrac{5*7+1*1}{5+1} )\\=(\dfrac{42}{6} ,\dfrac{36}{6} )\\P(x,y)=(7,6)$

The correct option is B.