What are the coordinates of the point on the directed line segment from (1,−6) to (8,8) that partitions the segment into a ratio of 4 to 3?

Step-by-step explanation:

Let's make this simple. Since we are given a ratio, that is the method we will use (as opposed to being told that the coordinate of the point that partitions the directed segment is one-third of the way from the first point to the second point. That's a different method). There is a formula for each of the coordinates we are looking for and they are:

  and   where

a = 4 (from the ratio),

b = 3 (from the ratio),

x1 = 1, y1 = -6,

x2 = 8, y2 = 8 (those are from the endpoints of the directed segment). Filling in to find x first:

which simplifies down to

and then y:

which simplifies down to

so the coorinates are (5, 2).

0 is its x and y coordinate