The end points of the diameter of a circle are ( 2,4) and ( -3 , -1 ) .Find its center.

The end points of the diameter of a circle are ( 2,4) and ( -3 , -1 ) .Find its center.

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  1. A(2,4) ———•——— B(-3,-1)

    [tex]\:\:\:\:\:\:\:\:\:\:\: {C(x,y)} [/tex]

    Using midpoint formula

    [tex]\sf{x = \dfrac{x1 + x2 }{2}}[/tex]

    [tex]\sf{x = \dfrac{2 + (-3) }{2}}[/tex]

    [tex]\pink\sf{x = \dfrac{-1}{2}}[/tex]

    And,

    [tex]\sf{y = \dfrac{y1 + y2 }{2}}[/tex]

    [tex]\sf{x = \dfrac{4 + (-1) }{2}}[/tex]

    [tex]\sf{x = \dfrac{3 }{2}}[/tex]

    Therefore , Co-ordinate of Center (C) is ([tex]\sf\dfrac{-1}{2} , \dfrac{3}{2}[/tex])

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