Which of the following can be possible orthocenter of the triangle:
Step-by-Step Solution
Key Concept: When orthocenter coincides with centroid, the triangle has special geometric properties that constrain its vertex positions.
The orthocenter equals the centroid of triangle $\triangle$. Computing $H_1 = \left(1, \sqrt{3}\right)$ using the orthocenter formula with coordinates summed appropriately, and $H_2 = (2, 0)$ using the centroid formula $\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}$. Two possible configurations yield these two points.
Correct Answer: 1