SOLUTION: if disatance between two points (a+2,3)and (5,-1) is 5 units,find the value of a.

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Question 742639: if disatance between two points (a+2,3)and (5,-1) is 5 units,find the value of a.
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
For convenience we work with d^2 instead of d


%0D%0Ad%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%0D%0A

becomes:
%0D%0A5%5E2=%285-%28a%2B2%29%29%5E2%2B%28-1-3%29%5E2%0D%0A


then

%0D%0A25=%283-a%29%5E2%2B%28-4%29%5E2%0D%0A
Notice that after we square a real quantity the result is positive so
(3-a)^2=(a-3)^2
and so we rewrite it as this:


%28a-3%29%5E2=25-16


%28a-3%29%5E2=9


abs%28a-3%29=3

this means a-3=3 or a-3=-3

and so a=6 or a=0

checking...
(5-(0+2))^2+(-1-3)^2=3^2+4^2
and so 0 works

(5-(6+2))^2+(-1-3)^2=(-3)^2+(-4)^2
and so does 6


:)