If orthocentre and circumcentre  of a \bigtriangleup are respectively (1,1) and (3,2) , then the coordinates of its  centroid  are 

  • Option 1)

    \left ( \frac{7}{5},\frac{5}{3} \right )

  • Option 2)

    \left ( \frac{5}{3},\frac{7}{3} \right )

  • Option 3)

    \left ( 7,5 \right )

  • Option 4)

    None

 

Answers (1)
D Divya Saini

 

Euler line -

In any non equilateral triangle the circumcentre (O), the centriod (G) and the orthocentre (H) are collinear and G divides OH in ratio 1:2

- wherein

 

 Cr = Centroid; Orthocentre\equiv H; Circumcentre \equiv 0

\frac{GO}{GH}=\frac{1}{2}                                 H\equiv (1, 1)

                                                   O\equiv (3, 2)

                                                 G\equiv (h, k)

\frac{2\times 3+1\times 1}{1+2} = h

\Rightarrow h=\frac{7}{3}

\frac{1\times 1+2\times 2}{1+2}=k

\Rightarrow k=\frac{5}{3}


Option 1)

\left ( \frac{7}{5},\frac{5}{3} \right )

This solution is correct

Option 2)

\left ( \frac{5}{3},\frac{7}{3} \right )

This solution is incorrect

Option 3)

\left ( 7,5 \right )

This solution is incorrect

Option 4)

None

This solution is incorrect

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