Question

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?

Answer 1

Answer:

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:

$x=\frac{bx_1+ax_2}{a+b}$   and   $y=\frac{by_1+ay_2}{a+b}$ 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:

$x=\frac{3(1)+4(8)}{4+3}$ which simplifies down to

$x=\frac{3+32}{7}=\frac{35}{7}=5$ and then y:

$y=\frac{3(-6)+4(8)}{4+3}$ which simplifies down to

$y=\frac{-18+32}{7}=\frac{14}{7}=2$ so the coorinates are (5, 2).