Question

If a triangle has its orthocenter at $(1,1)$ and circumcenter at $(\frac{3}{2},\frac{3}{4})$ then the co-ordinates of the centroid of the triangles are

• A. $(\frac{4}{3},-\frac{5}{6})$
• B. $(\frac{4}{3},\frac{5}{6})$
• C. $(-\frac{4}{3},\frac{5}{6})$
• D. $(-\frac{4}{3},-\frac{5}{6})$

Answer 1

The correct option is B $(\frac{4}{3},\frac{5}{6})$

(b) Since the centroid divides the line joining the orthocentre and circumcentre in the ratio $2:$ 1 internally ,

therefore if the centroid is $(x,y)$ then

$x=\frac{2.\frac{3}{2}+1.1}{2+1}=\frac{4}{3}$ and $y=\frac{2.\frac{3}{4}+1.1}{2+1}=\frac{5}{6}$

$\therefore$ Co-ordinates of centroid are $(\frac{4}{3},\frac{5}{6}).$