Question 1086099
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<pre>
The square of the distance from (x,4) to (5,-2) is 

{{{(5-x)^2 + ((-2)-4)^2}}} = {{{(5-x)^2 + (-6)^2}}} = {{{(5-x)^2 + 36}}}.

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

{{{(3-x)^2 + (4-4)^2}}} = {{{(3-x)^2 + 0^2}}} = {{{(3-x)^2 }}}.


So, you need to solve this equation

{{{(5-x)^2 + 36}}} = {{{(3-x)^2 }}},   or

{{{25 - 10x + x^2 + 36}}} = {{{9 - 6x + x^2}}},   or

61 - 10x = 9 - 6x,   or

61 - 9 = 10x - 6x,

4x = 52  ====>  x = {{{52/4}}} = 13.
</pre>

<U>Answer</U>.  x= 13.


Solved.