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If the two vertices of an equilateral tr...

If the two vertices of an equilateral triangle be `(0,0),(3,sqrt(3)),` find the third vertex.

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To find the third vertex of the equilateral triangle given the vertices \((0,0)\) and \((3,\sqrt{3})\), we can follow these steps: ### Step 1: Identify the Known Vertices We have two vertices of the equilateral triangle: - Vertex A: \((0, 0)\) - Vertex B: \((3, \sqrt{3})\) ### Step 2: Calculate the Length of Side AB ...
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Knowledge Check

  • If two vertices of an equilateral triangle are (1,1) and (-1,1) then the third vertex may be

    A
    `(-sqrt3,-sqrt3)`
    B
    `(-sqrt3,sqrt3)`
    C
    `(sqrt3,-sqrt3)`
    D
    `(sqrt3,sqrt3)`

  • If two vertices of an equilateral triangle are A (-a,0)and B (a,0), a gt 0, and the third vertex C lies above y-axis, then the equation of the circumcircle of Delta ABC is :

    A
    `3x ^(2) + 3y^(2) - 2 sqrt3 ay = 3a ^(2)`
    B
    `3x ^(2) + 3y ^(2) - 2ay = 3a ^(2)`
    C
    `x ^(2) +y ^(2) - 2ay =a ^(2)`
    D
    `x ^(2) +y ^(2) - sqrt3 ay =a ^(3)`

  • If (2,0) and (-2, 0) are the two vertices of an equilateral triangle , then the third vertex can be "_______" .

    A
    (0,0)
    B
    `( 2 , -2)`
    C
    `(0 , 2sqrt3)`
    D
    `(sqrt3 , sqrt3)`

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