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The length of the segment between the points (2a, a - 4) and (4,1) is 2*sqrt(30) units. What is the product of all possible values for a?

 Jul 24, 2021
 #1
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Using  the  square of  the distance formula

 

(4 - 2a)^2   +  (a - 4 - 1)^2   =    (2sqrt 30) ^2           simplify

 

16  - 16a  + 4a^2  +  ( a - 5)^2  =    4*30

 

16 - 16a  +  4a^2  + a^2  - 10a  +  25 =   120

 

5a^2  -  26a  + 41   = 120

 

5a^2  - 26a   -  79   =   0

 

This will have two solutions for  "a".....their  product  =   -79 / 5

 

cool cool cool

 Jul 25, 2021

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