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Question 1141315: Given a directed line segment with endpoints A(3,2) and B(6,11), what is the y- coordinate of C if AC:CB= 2:1?
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
AC:CB = 2:1 means C is two-thirds of the way from A to B.
Think of the x- and y-components separately to solve the problem.
The change in the x coordinates from A to B is 6-3 = 3; 2/3 of that is 2. So the x coordinate you are looking for is 2 more than the x-coordinate of A: 3+2=5.
The change in the y coordinates from A to B is 11-2 = 9, 2/3 of that is 6. So the y coordinate you are looking for is 6 more than the y-coordinate of A: 2+6=8.
ANSWER: (5,8)
Here is a different description of the process for solving the problem; perhaps this will make more sense to you.
To get from A to B, you need to move 6-3 = 3 units right and 11-2 = 9 units up.
You want to find the point that divides the segment into two parts in the ratio 2:1. So divide the "trip" from A to B into three equal parts. Each part is then 3/3 = 1 unit right and 9/3 = 3 units up.
Now start at A and move those two parts: (3,2)+(1,3) = (4,5); then (4,5)+(1,3) = (5,8).
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