SOLUTION: From A(0,1),B(2,1),C(4,3) and D(-2,5). Find the values of r and s if rAD + sCD =AB

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Question 849893: From A(0,1),B(2,1),C(4,3) and D(-2,5). Find the values of r and s if rAD + sCD =AB
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Some information is missing because that equation has two variables,
and there must be enough information to get another equation in order
to find a definite value for both variables.  We can find all the
distances so that the three lines' lengths are known, but that is
as far as we can take it without the missing information.  You may
post the missing information in the thank you note.  But here are how
to find the lengths of the three lines in the one equation: 



Use the distance formula to find the length of AD

d = √(x2-x1)²+(y2-y1 
 
where (x1,y1) = (0,1), (x2,y2) = (-2,5),  

AD = √(-2-0)²+(5-1)² = √(-2)²+(4)² = √4+16 = √20 = √4·5 = 2√5

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Use the distance formula to find the length of CD

d = √(x2-x1)²+(y2-y1 
 
where (x1,y1) = (4,3), (x2,y2) = (-2,5),  

AD = √(-2-4)²+(5-3)² = √(-6)²+(2)² = √36+4 = √40 = √4·10 = 2√10

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Use the distance formula to find the length of AB.
(We can look and see that this line has length 2.  But we'll
use the formula anyway:

d = √(x2-x1)²+(y2-y1 
 
where (x1,y1) = (0,1), (x2,y2) = (2,1),  

AB = √(-2-0)²+(1-1)² = √(-2)²+(0)² = √4+0 = √4 = 2

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rAD + sCD = AB

r·2√5 + s·2√10 = 2

or

2r√5 + 2s√10 = 2

And we can divide that equation through by 2:

r√5 + s√10 = 1

That's as far as we can go without the missing information.

Edwin