Question 228481: An equilateral triangle has 2 verticles at (0,-1) and (0,5) Find all possibilities for the third vertex.
I figured out the distance between the two points is 6 and I know that the thrid vertex can be in quadrant I and II, but I'm having trouble trying to use the distance formula figure out the coordinates of the vertex.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An equilateral triangle has 2 verticles at (0,-1) and (0,5) Find all possibilities for the third vertex.
I figured out the distance between the two points is 6 and I know that the thrid vertex can be in quadrant I and II, but I'm having trouble trying to use the distance formula figure out the coordinates of the vertex.
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Let (x,y) be 6 from (0,-1)
6^2 = (x-0)^2 + (y+1)^2
36 = x^2 + y^2+2y+1
A) 35 = x^2+y^2+2y
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Let (x,y) be 6 from (0,5)
6^2 = (x-0)^2 + (y-5)^2
36 = x^2 + y^2-10y+25
B) 9 = x^2 + y^2-10y
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Subtract Equation B from Equation A and solve for "y":
16 = 12y
y = 4/3
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Sustitute into "A" to solve for "x":
35 = x^2 + (16/9)+2(4/3)
35 = x^2 + 16/9 + 24/9
x^2 = 35 - (40/9)
x^2 = 275/9
x = (5/3)sqrt(11) or x = (-5/3)sqrt(11)
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Vertices are ((5/3)sqrt(11),4/3) or ((-5/3)sqrt(11),4/3)
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Cheers,
Stan H.
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