Answer:
(1, 2)
Step-by-step explanation:
The orthocenter of a triangle is the point of intersection of its three altitudes (line segments drawn from a vertex perpendicular to the opposite side).
In triangle ABG, vertices A and B share the same x-coordinate, which means side AB is vertical (parallel to the y-axis). Vertices A and G share the same y-coordinate, which means side AG is horizontal (parallel to the x-axis). Since sides AB and AG are perpendicular, triangle ABG is a right triangle with the right angle at vertex A.
In a right triangle, the coordinates of the orthocenter are the coordinates of the vertex that forms the right angle. This is because the altitudes drawn from each of the acute angles coincide with the legs of the right triangle. The legs intersect at the vertex of the right angle, and so the orthocenter is located at that vertex.
Therefore, the coordinates of the orthocenter of triangle ABG are:
[tex]\LARGE\boxed{\boxed{(1,2)}}[/tex]
