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The length of the segment between the points (2a,a - 4) and (4,1) is units 2*sqrt(10). What is the product of all possible values for a?

 Apr 11, 2021
 #1
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Using the distance formula

 

sqrt  [  ( 2a - 4)^2  +  ( a - 1 - 4)^2  ]  =  2sqrt 10

 

sqrt  [ ( 4a^2  - 16a + 16  +  ( a -5)^2  ]  = 2sqrt 10

 

sqrt  [ 4a^2  - 16a  + 16  + a^2  - 10a + 25  ]  =  2sqrt 10

 

sqrt [ 5a^2  - 26a + 41 ]  =  2sqrt 10        square  both sides

 

5a^2 - 26a  + 41  =  40

 

5a^2  - 26a  + 1 =  0 

 

In the form   ax^2 + bx + c........the product of  the  roots =   c / a

 

So....the product of  all possible  values of a     =    1 / 5

 

 

cool cool cool

 Apr 11, 2021

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