What are the coordinates of the point on the directed line segment from (- 3, - 9) to (4, 5) that partitions the segment into a ratio of 5 to 2?

(0,-1)

Step-by-step explanation:

Let the ends of the line segments be A(-4,3) and B(5,-6).

Ratio=4:5

By the concept of cordinate geometry,

x=(mx2+nx1)/(m+n)

y=(my2+ny1)/(m+n)

where m and n is the ratio m:n.

So, here the cordinates are

x={4(5)+5(-4)}/(4+5)

x=(20–20)/9

x=0

y={4(-6)+5(3)}/9

y={-24+15}/9

y=(-9)/9

y=(-1)

Therefore the cordinates of the point that divides the given line segment in the ratio 4 : 5 is (0,-1)

:)