The length of the segment between the points (2a,a - 4) and (4,1) is units 2*sqrt(10). What is the product of all possible values for a?
Usig the square of the distance formula
(2a - 4)^2 + (a - 4 - 1)^2 = (2sqrt (10) ) ^2
4a^2 - 16a + 16 + (a - 5)^2 = 4*10
4a^2 - 16a + 16 + a^2 - 10a + 25 = 40 simplify
5a^2 - 26a + 1 = 0
By Vieta.....the product of all possible values for a =
1 / 5
