SOLUTION: Hello, I'm having difficulty with this problem: The distance between (a,4) and (-3,-2) is (sqrt)61. I need help finding the two possible values for a. Thank you

Algebra ->  Algebra  -> Expressions-with-variables -> SOLUTION: Hello, I'm having difficulty with this problem: The distance between (a,4) and (-3,-2) is (sqrt)61. I need help finding the two possible values for a. Thank you      Log On

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Question 104408: Hello,

I'm having difficulty with this problem:

The distance between (a,4) and (-3,-2) is (sqrt)61. I need help finding the two possible values for a.

Thank you
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
The distance, d, between two points (x1,y1) and (x2,y2) is given by the following equation :
d%5E2=%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29
(a,4) and (-3,-2) is (sqrt)61
%28sqrt%2861%29%29%5E2=%28-3-a%29%5E2%2B%28-2-4%29%5E2
61=%28-3-a%29%5E2%2B36
25=%28-3-a%29%5E2
sqrt%2825%29=sqrt%28%28-3-a%29%5E2%29
There are two solutions possible since sqrt%2825%29 can be 5 or -5.
For 5,
5=-3-a
a=-8(-8,4)
for -5,
-5=-3-a
a=2(2,4)
drawing%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++grid%28+1+%29%2C%0D%0A++red%28+circle%28+-3%2C+-2%2C+.2+%29+%29%2C%0D%0A++blue%28+circle%28+2%2C+4%2C+.2+%29+%29%2Cblue%28+circle%28+-8%2C+4%2C+.2+%29+%29%0D%0A%29