What are the coordinates of the point on the directed line segment from (-8,-2) to (1,10) that partitions the segment into a ratio of 2 to 1?

Question

This question is related to partitioning in the math subject, geometry. I've been stuck on this question for over an hour.

Answer 1

Let x and y be coordinate of the point C that partitions the segment.

And Let A =(-8,-2) and B = (1,10)

So the ratio of AC to AB = 2:3     (Since 2+1=3, remember we are not taking ratio of AB:BC but we are taking AC:AB)

Given: partition the line segment in 2:1

So,

x = -8 + 2/3 {1- (-8)}

=> x = -8 +(2/3)(9)

=> x = -8 + 6

=>x = -2

Similarly,

y = -2 + (2/3){10-(-2)}

=> y = -2 + (2/3)(12)

=> y = -2 +8

=> y = 6

So the coordinate of the point is (-2,6)