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?
+128448 Using the distance formula
sqrt [ ( 2a - 4)^2 + ( a - 1 - 4)^2 ] = 2sqrt 10
sqrt [ ( 4a^2 - 16a + 16 + ( a -5)^2 ] = 2sqrt 10
sqrt [ 4a^2 - 16a + 16 + a^2 - 10a + 25 ] = 2sqrt 10
sqrt [ 5a^2 - 26a + 41 ] = 2sqrt 10 square both sides
5a^2 - 26a + 41 = 40
5a^2 - 26a + 1 = 0
In the form ax^2 + bx + c........the product of the roots = c / a
So....the product of all possible values of a = 1 / 5
