Answer:
It is not impossible for the centroid and the orthocenter of a triangle to be the same point.
Step-by-step explanation:
In a triangle, the centroid is the point of intersection of the three medians, which are the lines joining each vertex to the midpoint of the opposite side. The centroid is also known as the center of gravity of the triangle.
On the other hand, the orthocenter is the point of intersection of the three altitudes, which are the lines drawn from each vertex perpendicular to the opposite side.
In most cases, the centroid and the orthocenter are different points. However, there is one special type of triangle where they coincide, and that is an equilateral triangle. In an equilateral triangle, all three medians and altitudes are the same line segment, resulting in the centroid and the orthocenter being the same point.
To summarize, in general, the centroid and the orthocenter of a triangle are different points. But in the special case of an equilateral triangle, they coincide.
