1. Tardigrade
  2. Question
  3. Mathematics
  4. If coordinates of the circumcentre and the orthocentre of a triangle are respectively (5, 5) and (2, 2), then the coordinates of the centroid are

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If coordinates of the circumcentre and the orthocentre of a triangle are respectively $(5, 5)$ and $(2, 2)$, then the coordinates of the centroid are

KEAMKEAM 2015Straight Lines

Solution:

The circumcentre $O$, centroid $G$ and orthocentre $O^{\prime}$ of a triangle are collinear. $G$ divides $O^{\prime} O$ in the ratio $2: 1$.
Let the coordinates of $G$ be $(x, y)$.
Then, $\left(\frac{2 \times 5+1 \times 2}{2+1}, \frac{2 \times 5+1 \times 2}{2+1}\right) $
$=(x, y) \Rightarrow (x, y)=(4,4)$

Hence, coordinates of centroid are $(4,4)$.