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Two vertices of triangle are (1,2) …

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Two vertices of triangle are (1,2) and (3,5). If the centroid of the triangle is at origin, find the coordinates of third vertex.

    • Posted by Zoya Khan 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Let the coordinates of the third vertex be (x, y), Then
    Coordinates of centroid of triangle are
    {tex}\left( {\frac{{x + 1 + 3}}{3},\frac{{y + 2 + 5}}{3}} \right){/tex}
    We have centroid is at origin (0, 0)
    {tex}\therefore \frac{{x + 1 + 3}}{3} = 0{/tex} and {tex}\frac{{y + 2 + 5}}{3} = 0{/tex}
    {tex}\Rightarrow{/tex} x + 4 = 0 {tex}\Rightarrow{/tex} y + 7 = 0
    {tex}\Rightarrow{/tex} x = -4 {tex}\Rightarrow{/tex} y = -7
    Hence, the coordinates of the third vertex are (-4, -7).

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