SOLUTION: Find all values of x so that the distant beetween the points (x,-1) and (2,5) is 2*square root 10

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Question 474008: Find all values of x so that the distant beetween the points (x,-1) and (2,5) is 2*square root 10
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find all values of x so that the distant be+tween the points (x,-1) and (2,5) is 2*square root 10
:
The distance formula: d = sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29
x1=x, y1=-1
x2=2, y2=5
:
sqrt%28%282-x%29%5E2%2B%285-%28-1%29%29%5E2%29 = 2sqrt%2810%29
:
sqrt%28%284-4x%2Bx%5E2%29%2B%286%29%5E2%29 = 2sqrt%2810%29
:
sqrt%28x%5E2+-+4x+%2B+4+%2B+36%29 = 2sqrt%2810%29
:
sqrt%28x%5E2+-+4x+%2B+40%29 = 2sqrt%2810%29
Square both sides
x^2 - 4x + 40 = 4(10)
x^2 - 4x + 40 = 40
x^2 - 4x + 40 - 40 = 0
x^2 - 4x = 0
Factor out x
x(x-4) = 0
Two solutions
x = 0
and
x = 4
:
See if that works for x=4
sqrt%28%282-4%29%5E2%2B%285-%28-1%29%29%5E2%29 = 2sqrt%2810%29
sqrt%28%28-2%29%5E2%2B%286%29%5E2%29 = 2sqrt%2810%29
sqrt%284%2B36%29%29 = 2sqrt%2810%29
sqrt%2840%29%29 = 2sqrt%2810%29
which is
sqrt%284%2A10%29%29 = 2sqrt%2810%29
factor out the square root of 4
2sqrt%2810%29%29 = 2sqrt%2810%29; ); OK
:
What about x= 0
sqrt%28%282-0%29%5E2%2B%285-%28-1%29%29%5E2%29 = 2sqrt%2810%29
sqrt%284%2B36%29 = 2sqrt%2810%29; this will work too
:
The solutions, x = 4, x = 0