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Two vertices of an equilateral triangle ...

Two vertices of an equilateral triangle are `(0, 0) and (0,2 sqrt(3))`. Find the third vertex

Text Solution

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The correct Answer is:
`(3,sqrt(3))`, `(-3,sqrt(3))`
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Knowledge Check

  • 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)`

  • Two vertices of an equilateral triangle are (-1,0) and (1,0), and its third vertex lies above the x-axis. The equation of its circumcircle is

    A
    `x^(2)+y^(2)+(2x)/(sqrt(3))-1=0`
    B
    `x^(2)+y^(2)-(2x)/(sqrt(3))-1=0`
    C
    `x^(2)+y^(2)+(2y)/(sqrt(3))-1=0`
    D
    `x^(2)+y^(2) -(2y)/(sqrt(3))-1=0`

  • 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)`

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    Conider the following for the next two (02 items that follow) The two vertices of an equilateral triangle are [0.0] and [2,2]. 1. The third vertex has least one irrational coordinate 2. The area is irrational Which of the above statements is/are correct?

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