what are the coordinates of the point on the directed line segment from (-8,8) to (7,-7) that partitons the segment into a ration of 3 to 2?

Answer 1

(-8,8) to (7,-7)

-8 to 7 is 15 units and 8 to -7 is also 15 units

3/5 of 15 is 9

-8+9=1 for x because you're going in the positive direction (-8 to 7)

8-9=-1 for y because you're going in the negative direction (8 to -7)

The point is ((1,-1). This divides the segment into a 3:2 ratio

check: find the length of the segment using the distance formula and you get SQRT(450)=15SQRT(2)

find the distance from (-8,8) to (1,-1) and you get 9SQRT(2)

find the distance from (1,-1) to (7,-7) and you get 6SQRT(2)

9SQRT(2)/6SQRT(2)=9/6=3/2