SOLUTION: if (x 4) is equidistant from (5 -2) and (3 4) find x

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Question 1086099: if (x 4) is equidistant from (5 -2) and (3 4) find x
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
The square of the distance from (x,4) to (5,-2) is 

%285-x%29%5E2+%2B+%28%28-2%29-4%29%5E2 = %285-x%29%5E2+%2B+%28-6%29%5E2 = %285-x%29%5E2+%2B+36.

The square of the distance from (x,4) to (3,4) is 

%283-x%29%5E2+%2B+%284-4%29%5E2 = %283-x%29%5E2+%2B+0%5E2 = %283-x%29%5E2+.


So, you need to solve this equation

%285-x%29%5E2+%2B+36 = %283-x%29%5E2+,   or

25+-+10x+%2B+x%5E2+%2B+36 = 9+-+6x+%2B+x%5E2,   or

61 - 10x = 9 - 6x,   or

61 - 9 = 10x - 6x,

4x = 52  ====>  x = 52%2F4 = 13.

Answer. x= 13.

Solved.