SOLUTION: Hi, I've got this word problem that I can't understand: Find the point of the line passing through A (-1,-1) and B (4,4) which is a.) twice as far from A as from B. (show two

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Hi, I've got this word problem that I can't understand: Find the point of the line passing through A (-1,-1) and B (4,4) which is a.) twice as far from A as from B. (show two      Log On

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Question 931686: Hi, I've got this word problem that I can't understand:
Find the point of the line passing through A (-1,-1) and B (4,4) which is
a.) twice as far from A as from B. (show two cases)
b.) three times as far from B as from A. (show two cases)
Thank you kindly in advance.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Calculate the distance from A to B.
Split it into thirds.
Calculate the point (2/3) of the distance from A or equivalently (1/2) of the distance from B.
D%5E2=%28-1-4%29%5E2%2B%28-1-4%29%5E2
D%5E2=2%2A%28-5%29%5E2
D%5E2=50
Since the slope of the line from A to B is 1 so change in x is equal to change in y.
x%5E2%2By%5E2=50
x%5E2%2Bx%5E2=50
2x%5E2=50
x=y=5
Two thirds from A would be,
DELTA%2Ax=DELTA%2Ay=%282%2F3%295=10%2F3
a)(-1%2B10%2F3,-1%2B10%2F3)=(-3%2F3%2B10%2F3,-3%2F3%2B10%2F3)=(7%2F3,7%2F3)
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Three times as far means break the distance into 4.
Three fourths from B would be (going backwards makes it negative),
DELTA%2Ax=DELTA%2Ay=-%283%2F4%295=-15%2F4
b)(4-15%2F4,4-15%2F4)=(16%2F4-15%2F4,16%2F4-15%2F4)=(1%2F4,1%2F4)
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