Question 1026569: please help me to solve the problem that is
The base of an equilateral triangle is x+y-2=0 and the opposite vertex is (2,-1) then find the equations of remaining sides of an equilateral triangle.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! please help me to solve the problem that is
The base of an equilateral triangle is x+y-2=0 and the opposite vertex is (2,-1) then find the equations of remaining sides of an equilateral triangle.
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Sketch the line y = -x+2
Plot the point (2,-1)
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Draw a line segment from (2,-1) perpendicular to the line y = -x+2
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Find the pt of intersection or base of that altitude.
y = mx + b
m = 1
-1 = 2 + b
b = -3
Eq:: y = x - 3
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System::
y = x - 3
y = -x+2
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Add and solve for "y"::
2y = -1
y = -1/2
Solve for "x"::
x-3 = -x+2
2x = 5
x = 5/2
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Plot the point (5/2,-1/2)
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Find the distance from (2,-1) to (5/2,-1/2) ; I'll call it "d".
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Sketch the equilateral triangle described in your problem
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Note: Each of the angles of that triangle is 60 degrees.
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sin(60) = d/(side of the equilateral triangle)
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Solve for the side value.
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Cheers,
Stan H.
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