What are the coordinates of the point on the directed line segment from (- 10, - 10) to (6, - 2) that partitions the segment into a ratio of 3 to 5

Denote:

A(-10, -10)  

B(6, -2)

vector AB(6 - -10, -2 - -10) = (16, 8)

(3/5)vector AB = (16 x 3/5, 8 x 3/5) = (9.6, 4.8)

=> Point M that partitions the directed line segment AB into a ratio of 3 to 5:

M = A + (3/5)vector AB = (-10 + 9,6, -10 + 4.8) = (-0.4, -5.2)

Hope this helps!

:)

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