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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 $a.$

 May 14, 2024
 #1
avatar+129491 
+1

Square of the distance formula

 

(a - 2)^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

 

Sum of possible a's  =  -(-28) / 5  =  28 / 5

 

cool cool cool

 May 14, 2024

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