Answer:
(2, -2)
Step-by-step explanation:
The difference of coordinates is ...
(6, -7) -(-6, 8) = (12, -15)
The point of interest is located 2/(2+1) = 2/3 of this distance from the first point. So, the point of interest is ...
first point + 2/3 distance
= (-6, 8) + (2/3)(12, -15)
= (-6, 8) + (8, -10)
= (2, -2)
_____
In symbolic terms, the point P that is 2/3 of the distance from A to B is ...
P = A + (2/3)(B -A) = (1/3)A +(2/3)B
P = (A +2B)/3
Filling in the coordinate values, we find ...
P = ((-6, 8) +2(6, -7))/3 = (-6+12, 8-14)/3 = (6, -6)/3
P = (2, -2)
