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avatar+1671 

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 $a.$

 Jan 16, 2024
 #1
avatar+128448 
+1

Using the 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 possile a's  =  28  / 5

 

cool cool cool

 Jan 16, 2024

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