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The length of the segment between the points (2a, a - 4) and (4,-7) is 2*sqrt(2) units. What is the product of all possible values for a?

 Jul 7, 2022
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Using the square of the distance formula

 

(2a - 4)^2  + ( a - 4 - -7)^2  =  (2 sqrt 2)^2

 

( 2a - 4)^2 + ( a +3)^2  = 8

 

4a^2 - 16a + 16 + a^2 +6a + 9 = 8

 

5a^2 -  10a + 17 = 0

 

This will not produce  real number values for "a"

 

But....the product of all possible values for "a" =   17 / 5

 

 

cool cool cool

 Jul 7, 2022

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