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avatar+1002 

The distance between the points $A$ and $B$ is $\sqrt{5}.$ If $A = (a,-1)$ and $B = (2,2a-7),$ then find the sum of all possible values of $a.$

 Mar 4, 2024
 #1
avatar+128406 
+1

Using the square of the distance  formula

 

(2 - a)^2  + (2a - 7 - -  1 )^2  = 5

 

(a - 2)^2  + (2a - 6)^2   = 5

 

a^2 - 4a + 4 + 4a^2 - 24a + 36  =  5

 

5a^2 - 28a + 35  =  0

 

The sum of the values for a  =   - (-28) / 5   =  28 / 5

 

cool cool cool

 Mar 4, 2024

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