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The circumcentre of a triangle whose vertices are (-2, -3), (-1, 0), (7, -6)​

By Anna

The circumcentre of a triangle whose vertices are (-2, -3), (-1, 0), (7, -6)​

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most of the are fish in the pond of his village were gradually dying. the waste of a factory in their village is flowing into the

2 thoughts on “The circumcentre of a triangle whose vertices are (-2, -3), (-1, 0), (7, -6)​”

  1. Let (x, y) be the circumcenter, which is equidistant from the vertices of the triangle (-2, -3), (-1, 0) and (7, -6) each.

    Let the distance be d. So, by distance formula,

    [tex]\longrightarrow d^2=(x+2)^2+(y+3)^2[/tex]

    [tex]\longrightarrow d^2=x^2+y^2+4x+6y+13\quad\quad\dots(1)[/tex]

    and,

    [tex]\longrightarrow d^2=(x+1)^2+(y-0)^2[/tex]

    [tex]\longrightarrow d^2=x^2+y^2+2x+1\quad\quad\dots(2)[/tex]

    and,

    [tex]\longrightarrow d^2=(x-7)^2+(y+6)^2[/tex]

    [tex]\longrightarrow d^2=x^2+y^2-14x+12y+85\quad\quad\dots(3)[/tex]

    Equating (1) and (2),

    [tex]\longrightarrow x^2+y^2+4x+6y+13=x^2+y^2+2x+1[/tex]

    [tex]\longrightarrow x=-3y-6\quad\quad\dots(4)[/tex]

    Equating (2) and (3),

    [tex]\longrightarrow x^2+y^2+2x+1=x^2+y^2-14x+12y+85[/tex]

    [tex]\longrightarrow 16x-12y-84=0[/tex]

    Putting value of from (4),

    [tex]\longrightarrow 16(-3y-6)-12y-84=0[/tex]

    [tex]\longrightarrow -60y-180=0[/tex]

    [tex]\longrightarrow y=-3[/tex]

    Then from (4),

    [tex]\longrightarrow x=-3(-3)-6[/tex]

    [tex]\longrightarrow x=3[/tex]

    Hence the circumcenter of the triangle is (x, y) = (3, -3).

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