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A point $(2, n)$ is 5 units away from the point $(-1, 1)$. What is the product of all possible integer values for $n$?

 Jan 15, 2021
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Use the distance formula (squared)

 

(2 - -1)^2  + ( 1 - n)^2   =   25          simplify

 

9  + n^2  - 2n + 1   =  25

 

n^2  - 2n + 10  =  25

 

n^2 - 2n  -  15  =  0        factor 

 

(n - 5) ( n + 3)  =  0

 

 

Setting each factor to 0and solving for  n produces   n = 5   and  n =  -3

 

Their product =  -15

 

 

cool cool cool

 Jan 15, 2021

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