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A line segment of length 5  has one endpoint at (1,2) and the other endpoint at (4,a) . Find all possible values of a, separated by commas.

 Apr 18, 2019
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Using the distance formula

 

5  = √[ ( 4 - 1)^2 + ( a - 2)^2 ]      square both sides

 

25  =(4 - 1)^2 + (a - 2)^2

 

25  = 3^2 + (a - 2)^2

 

25 = 9 + (a - 2)^2      subtract 9 from both sides

 

16  = (a - 2)^2       take both roots

 

±√16  = a - 2

 

± 4  = a - 2

 

So either

 

a - 2  =  4       ⇒   a  = 6

 

Or

 

a - 2 = - 4  ⇒   a = -2

 

 

cool cool cool

 Apr 18, 2019

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