Question

If co-ordinates of orthocentre and centroid of a triangle are

(4, –1) and (2, 1) then co-ordinates of a point which is equidistance from the vertices of the triangle is-

• A. (2, 2)
• B. (3, 2)
• C. (2, 3)
• D. None

Answer 1

Answer: (D)

None

Answer 2

Centroid divides line joining orthocentre and

circumcentre in the ratio 2 : 1

Let circumcentre be (x, y)

\begin{tabular} { c c c } & 2 \ \hline $( 4 , - 1 )$ & $( 2,1 )$ & $( \mathrm { x } , \mathrm { y } )$ \end{tabular}

$\frac{2x + 4}{2 + 1}$ = 2 Ž x = 1

and $\frac{2y - 1}{2 + 1}$ = 1 Ž y = 2

Circumcentre (1, 2)