Question

What are the coordinates of the point on the directed line segment from (−8,−6) to (-1, 8) that partitions the segment into a ratio of 5 to 2?

Answer 1

`\\ \rm\Rrightarrow M(x,y)`

`\\ \rm\Rrightarrow\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)`

`\\ \rm\Rrightarrow\left((-5-16)/(7),(40-12)/(7)\right)`

`\\ \rm\Rrightarrow\left((-21)/(7),(28)/(7)\right)`

`\\ \rm\Rrightarrow(-3,4)`

Answer 2

(-3, 4)

Explanation:

let the point P(x, y)

x = (5/7 × (-1+8)) + (-8)

= (5/7 × 7) -8 = 5-8 = -3

y = (5/7 × (8+6)) + (-6)

= (5/7 × 14) -6 = 10-6 = 4

so, P => (-3 , 4)