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)