Question

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

$(\frac{4}{3},\frac{5}{6})$

Since the centroid divides the line joining the orthocenter and circumcenter in the ratio 2:1 internally,

Therefore, if the centroid is (x, y), then

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

$\therefore$ Coordinates of centroid are $(\frac{4}{3},\frac{5}{6})$