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 $a.$
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
+1439 
