A line segment of length 5 has one endpoint at (1,2) and the other endpoint at (4,a) . Find all possible values of a, separated by commas.
+128406 Using the distance formula
5 = √[ ( 4 - 1)^2 + ( a - 2)^2 ] square both sides
25 =(4 - 1)^2 + (a - 2)^2
25 = 3^2 + (a - 2)^2
25 = 9 + (a - 2)^2 subtract 9 from both sides
16 = (a - 2)^2 take both roots
±√16 = a - 2
± 4 = a - 2
So either
a - 2 = 4 ⇒ a = 6
Or
a - 2 = - 4 ⇒ a = -2
