Question

find the point which divides the segment from (-5,-4) to (6,-2) in the ratio 2:3

Answer 1

make a sketch and let our point needed be (x,y)

for the x:
(x-(-5))/(6-x) = 2/3
3x + 15 = 12-2x
5x = -3
x = -3/5

for the y:
(y+4)/(-2-y) = 2/3
3y + 12 = -4-2y
5y = -16
y = -16/5

your point is (-3/5 , -16/5)

or, using vectors

(x,y) = (3/5)(-5,-4) + (2/5)(6,-2)
= (-3 , -12/5) + (12/5, -4/5)
= (-3/5 , -16/5)