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If the vertices of a triangle have ratio...

If the vertices of a triangle have rational coordinates, then prove that the triangle cannot be equilateral.

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The correct Answer is:
True
We know that, if the verticles of a triangle have integral coordinates, then the triangle cannot be equilateral. Hence, the given statements is true.
Since, in equilatteral triangle, we get `tan 60^@=sqrt3` =slope of the line, so with integral coordinates as vertices, the triangle cannot be equilateral.
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Knowledge Check

  • If the vertices of a triangle have integral coordinates, then the triangle is

    A
    equilateral
    B
    never equilateral
    C
    always isosceles
    D
    None of these

  • If each of the vertices of a triangle has integral coordinates, then the triangles may be

    A
    right angled
    B
    equilateral
    C
    isosceles
    D
    scalene

  • If two vertices of an equilaterla triangle have integral coordinates, then the third vetex will have

    A
    integral coodinates which are rtional
    B
    coordinates which are rational
    C
    at least one coordinate irrational
    D
    coordinates which are irrational

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    Statement 1: If the vertices of a triangle are having rational coordinates,then its centroid, circumcenter,and orthocentre are rational. Statement 2: In any triangle,orthocentre, centroid,and circumcenter are collinear,and the centroid divides the line joining the orthocentre and circumcenter in the ratio 2:1.

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