SOLUTION: If(x,4) is equidistant to (5,-2) and (3,4) find the x

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Question 1176758: If(x,4) is equidistant to (5,-2) and (3,4) find the x
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If(x,4) is equidistant to (5,-2) and (3,4)
means distance between (x,4) and (5,-2) is same as distance between (x,4) and (3,4)

to find the x, use distance formula

distance between (x,4) and (5,-2) is:
d=sqrt%28%28x-5%29%5E2%2B%284-%28-2%29%29%5E2%29
d=sqrt%28%28x-5%29%5E2%2B%284%2B2%29%5E2%29
d=sqrt%28%28x-5%29%5E2%2B36%29......eq.1
distance between (x,4) and (3,4) is:
d=sqrt%28%28x-3%29%5E2%2B%284-4%29%5E2%29
d=sqrt%28%28x-3%29%5E2%2B%280%29%5E2%29
d=sqrt%28%28x-3%29%5E2%29......eq.2
from eq.1 and eq.2 we have
sqrt%28%28x-5%29%5E2%2B36%29=sqrt%28%28x-3%29%5E2%29....square both sides
%28x-5%29%5E2%2B36=%28x-3%29%5E2.....expend
x%5E2-10x%2B25%2B36=x%5E2-6x%2B9
cross%28x%5E2%29-10x%2B61=cross%28x%5E2%29-6x%2B9
-10x%2B61=-6x%2B9
-9%2B61=10x-6x
52=4x
x=52%2F4
x=13

so, the point is (13,4)







Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

If(x,4) is equidistant to (5,-2) and (3,4) find the x
Distance (d) from (x, 4) to (5, - 2):  Distance (d) from (x, 4) to (3, 4): 

Therefore,