The length of the segment between the points (2a, a-4) and (3, -1) is sqrt(26) units. What is the product of all possible values for a?
+129849 Using the square of the distance formula we have that
( 2a -3)^2 + ( a -4 - (- 1) )^2 = 26 simplify
(2a - 3)^2 + ( a - 3)^2 = 26
4a^2 - 12a + 9 + a^2 - 6a + 9 = 26
5a^2 - 18a - 8 = 0 factor
(5a + 2) (a - 4) = 0
Set each factor to 0 and solve for a
5a + 2 = 0 a - 4 = 0
5a = -2 a = 4
a = -2/5
And the product is (4) ( -2/5) = -8/5
