SOLUTION: the segment A(-1,4) to B(2,-2) is extended three times its own length. the terminal point is.

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Question 1047766: the segment A(-1,4) to B(2,-2) is extended three times its own length. the terminal point is.
Found 2 solutions by advanced_Learner, AnlytcPhil:
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
sorry i was in a hurry,hope this clears up.
the lenght of AB is sqrt%2845%29
three times is 3sqrt%2845%29
slope of the line is m=-2x%2B2
use distance formula for A(-1,4) or B(2,-2)
using B(2,-2)
%28x-2%29%5E2%2B%28-2x%2B2%2B2%29%5E2}=%283sqrt%2845%29%29%5E2
simplify to get
%28x%5E2-4x-77%29=0

using A(-1,4)
%28x%2B1%29%5E2%2B%28-2x%2B2-4%29%5E2=%283sqrt%2845%29%29%5E2
Simplify to get
%28x%5E2%2B2x-80%29=0

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!

The other tutor's answer is wrong.

There are two answers.  I'll find one of them for you, and
you can find the other answer yourself.  One answer is when 
we extend it upward from A(-1,4), and the other is when we 
extend it downward from B(2,-2).

I'll extend it downward and get that answer.  Then you can extend it
upward to get the other answer:



The trick is to observe that when we go from A(-1,4) down to B(2,-2),
we go 3 units right and 6 units down, indicated by the blue lines.
So we first extend the line to twice its length, by going 3 units
right from (2,-2) and 6 units down. 



Finally, we extend the line to three times its length, by going 3 units
right from (5,-8) and 6 units down.



So one answer is (8,-14).  You can find the other answer
by extending it upward from A(-1,4).

Edwin