Find the sum of all values of a such that the point (a,21) is 10 sqare root 2 from the point (4,7).
+23245 Distance Formula: Distance = sqrt[ (x2 - x1)2 + (y2 - y1)2 ]
Let (x1, y1) = (a, 21) and (x2, y2) = (4,7)
Distance = sqrt[ (x2 - x1)2 + (y2 - y1)2 ]
---> 10·sqrt(2) = sqrt[ (4 - a)2 + (7 - 21)2 ]
---> 10·sqrt(2) = sqrt[ (4 - a)2 + (-14)2 ]
---> 10·sqrt(2) = sqrt[ (4 - a)2 + 196 ]
square both sides:
---> 100·2 = (4 - a)2 + 196
---> 200 = (4 - a)2 + 196
---> 4 = (4 - a)2
take the square root of both sides:
---> Either 4 - a = 2 or 4 - a = -2
---> Either a = 2 or a = 6
Summing the two answers: 2 + 6 = 8
